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A fast linearized virtual element method on graded meshes for nonlinear time-fractional diffusion equations

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Lévy-driven stochastic Volterra integral equations with doubly singular kernels: existence, uniqueness, and a fast EM method

Advances in Computational Mathematics, Vol. 46 (2020), Iss. 2

Parareal algorithms with local time-integrators for time fractional differential equations

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A fast algorithm for simulation of rough volatility models

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The stability analysis and numerical simulation based on Sinc Legendre collocation method for solving a fractional epidemiological model of the Ebola virus

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Partial Differential Equations in Applied Mathematics, Vol. 3 (2021), Iss. P.100037

Magnetohydrodynamic Analysis and Fast Calculation for Fractional Maxwell Fluid with Adjusted Dynamic Viscosity

Magnetochemistry, Vol. 10 (2024), Iss. 10 P.72

Second-order nonuniform time-stepping schemes for time-fractional evolution equations with general elliptic operator

Applied Mathematics Letters, Vol. 139 (2023), Iss. P.108541

Adaptive Second-Order Crank--Nicolson Time-Stepping Schemes for Time-Fractional Molecular Beam Epitaxial Growth Models

SIAM Journal on Scientific Computing, Vol. 42 (2020), Iss. 3 P.B738

A second-order fast compact scheme with unequal time-steps for subdiffusion problems

Numerical Algorithms, Vol. 86 (2021), Iss. 3 P.1011

Adaptive linear second-order energy stable schemes for time-fractional Allen-Cahn equation with volume constraint

Communications in Nonlinear Science and Numerical Simulation, Vol. 90 (2020), Iss. P.105366

Fast L2-1σ Galerkin FEMs for generalized nonlinear coupled Schrödinger equations with Caputo derivatives

Applied Mathematics and Computation, Vol. 416 (2022), Iss. P.126734

Finite element methods for fractional diffusion equations

International Journal of Modeling, Simulation, and Scientific Computing, Vol. 11 (2020), Iss. 04 P.2030001

Finite Difference/Finite Element Method for Tempered Time Fractional Advection–Dispersion Equation with Fast Evaluation of Caputo Derivative

Journal of Scientific Computing, Vol. 83 (2020), Iss. 3

Unconditional Convergence of a Fast Two-Level Linearized Algorithm for Semilinear Subdiffusion Equations

Journal of Scientific Computing, Vol. 80 (2019), Iss. 1 P.1

Clown face in 3D chaotic system integrated with memristor electronics, DNA encryption and fractional calculus

The European Physical Journal B, Vol. 97 (2024), Iss. 5

An Efficient Mechanism to Solve Fractional Differential Equations Using Fractional Decomposition Method

Symmetry, Vol. 13 (2021), Iss. 6 P.984

Local discontinuous Galerkin methods for the time tempered fractional diffusion equation

Applied Mathematics and Computation, Vol. 365 (2020), Iss. P.124725

A time two-grid algorithm for two-dimensional nonlinear time-fractional partial integro-differential equations

Mathematics and Computers in Simulation, Vol. 221 (2024), Iss. P.550

Linearized fast time-stepping schemes for time–space fractional Schrödinger equations

Physica D: Nonlinear Phenomena, Vol. 454 (2023), Iss. P.133865

Unconditional optimal error bounds of the fast nonuniform Alikhanov scheme for a nonlinear time-fractional biharmonic equation

Journal of Applied Mathematics and Computing, Vol. 70 (2024), Iss. 5 P.4053

Mathematical modeling and stability analysis of the novel fractional model in the Caputo derivative operator: A case study

Heliyon, Vol. 10 (2024), Iss. 5 P.e26611

Unconditionally optimal H1-error estimate of a fast nonuniform L2-1σ scheme for nonlinear subdiffusion equations

Numerical Algorithms, Vol. 92 (2023), Iss. 3 P.1655

The fast method and convergence analysis of the fractional magnetohydrodynamic coupled flow and heat transfer model for the generalized second-grade fluid

Science China Mathematics, Vol. 67 (2024), Iss. 4 P.919

Two-grid finite element methods for nonlinear time-fractional parabolic equations

Numerical Algorithms, Vol. 90 (2022), Iss. 2 P.709

A fast implicit difference scheme for solving the generalized time–space fractional diffusion equations with variable coefficients

Numerical Methods for Partial Differential Equations, Vol. 37 (2021), Iss. 2 P.1136

$$H^1$$-analysis of H3N3-2$$_\sigma $$-based difference method for fractional hyperbolic equations

Computational and Applied Mathematics, Vol. 43 (2024), Iss. 1

A fast Euler-Maruyama method for fractional stochastic differential equations

Journal of Applied Mathematics and Computing, Vol. 69 (2023), Iss. 1 P.273

Asymptotically compatible energy of variable-step fractional BDF2 scheme for the time-fractional Cahn–Hilliard model

IMA Journal of Numerical Analysis, Vol. (2024), Iss.

Local error estimates of the fourth-order compact difference scheme for a time-fractional diffusion-wave equation

Computers & Mathematics with Applications, Vol. 142 (2023), Iss. P.283

High-Order Local Discontinuous Galerkin Algorithm with Time Second-Order Schemes for the Two-Dimensional Nonlinear Fractional Diffusion Equation

Communications on Applied Mathematics and Computation, Vol. 2 (2020), Iss. 4 P.613

A fast Euler–Maruyama method for Riemann–Liouville stochastic fractional nonlinear differential equations

Physica D: Nonlinear Phenomena, Vol. 446 (2023), Iss. P.133685

A fast method for variable-order Caputo fractional derivative with applications to time-fractional diffusion equations

Computers & Mathematics with Applications, Vol. 80 (2020), Iss. 5 P.1443

A class of time-fractional diffusion equations with generalized fractional derivatives

Journal of Computational and Applied Mathematics, Vol. 414 (2022), Iss. P.114424

A Comparison of a Priori Estimates of the Solutions of a Linear Fractional System with Distributed Delays and Application to the Stability Analysis

Axioms, Vol. 10 (2021), Iss. 2 P.75

Space–time finite element method for the multi-term time–space fractional diffusion equation on a two-dimensional domain

Computers & Mathematics with Applications, Vol. 78 (2019), Iss. 5 P.1367

Couple Stress Sodium Alginate-Based Casson Nanofluid Analysis through Fick’s and Fourier’s Laws with Inclined Microchannel

Journal of Function Spaces, Vol. 2023 (2023), Iss. P.1

Fast algorithm based on the novel approximation formula for the Caputo-Fabrizio fractional derivative

AIMS Mathematics, Vol. 5 (2020), Iss. 3 P.1729

Fast compact finite difference schemes on graded meshes for fourth-order multi-term fractional sub-diffusion equations with the first Dirichlet boundary conditions

International Journal of Computer Mathematics, Vol. 100 (2023), Iss. 2 P.361

A Stable Fast Time-Stepping Method for Fractional Integral and Derivative Operators

Journal of Scientific Computing, Vol. 77 (2018), Iss. 1 P.283

Equivalence between a time-fractional and an integer-order gradient flow: The memory effect reflected in the energy

Advances in Nonlinear Analysis, Vol. 12 (2022), Iss. 1

Fast high-order linearized exponential methods for efficient simulation of 2D time-fractional Burgers equation in polymer solution dynamics

Journal of Mathematical Chemistry, Vol. (2024), Iss.

A fast modified $$\overline{L1}$$ finite difference method for time fractional diffusion equations with weakly singular solution

Journal of Applied Mathematics and Computing, Vol. 70 (2024), Iss. 4 P.3631

A fast H3N3‐2σ$_\sigma$‐based compact ADI difference method for time fractional wave equations

Du, Ruilian

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. (2024), Iss.

Reduced proper orthogonal decomposition spectral element method for the solution of 2D multi-term time fractional mixed diffusion and diffusion-wave equations in linear and nonlinear modes

Computers & Mathematics with Applications, Vol. 117 (2022), Iss. P.127

Long time numerical behaviors of fractional pantograph equations

Mathematics and Computers in Simulation, Vol. 172 (2020), Iss. P.244

Fast Evaluation of Artificial Boundary Conditions for Advection Diffusion Equations

SIAM Journal on Numerical Analysis, Vol. 58 (2020), Iss. 6 P.3530

Highly efficient schemes for time-fractional Allen-Cahn equation using extended SAV approach

Numerical Algorithms, Vol. 88 (2021), Iss. 3 P.1077

Mathematical analysis and efficient finite element approximation for variable‐order time‐fractional reaction–diffusion equation with nonsingular kernel

Mathematical Methods in the Applied Sciences, Vol. 46 (2023), Iss. 7 P.8074

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1

A Novel Spectral Method for the Subdiffusion Equation

2023

A High-Order Discrete Energy Decay and Maximum-Principle Preserving Scheme for Time Fractional Allen–Cahn Equation

Journal of Scientific Computing, Vol. 96 (2023), Iss. 2

Compatible Energy Dissipation of the Variable-Step \({\boldsymbol{L1}}\) Scheme for the Space-Time Fractional Cahn-Hilliard Equation

SIAM Journal on Scientific Computing, Vol. 45 (2023), Iss. 5 P.A2539

Fast and efficient finite difference/finite element method for the two-dimensional multi-term time-space fractional Bloch-Torrey equation

Applied Mathematics and Computation, Vol. 398 (2021), Iss. P.125985

Fast evaluation and robust error analysis of the virtual element methods for time fractional diffusion wave equation

Computers & Mathematics with Applications, Vol. 177 (2025), Iss. P.41

A Lagrangian relaxation towards equilibrium wall model for large eddy simulation

Journal of Fluid Mechanics, Vol. 934 (2022), Iss.

Error analysis of arbitrarily high-order stepping schemes for fractional integro-differential equations with weakly singular kernels

Nonlinear Engineering, Vol. 13 (2024), Iss. 1

Fast algorithms for convolution quadrature of Riemann-Liouville fractional derivative

Applied Numerical Mathematics, Vol. 145 (2019), Iss. P.384

A scale-dependent hybrid algorithm for multi-dimensional time fractional differential equations

Fractional Calculus and Applied Analysis, Vol. 25 (2022), Iss. 5 P.2062

Stability and superconvergence of efficient MAC schemes for fractional Stokes equation on non-uniform grids

Applied Numerical Mathematics, Vol. 138 (2019), Iss. P.30

Fourier's and Fick's laws analysis of couple stress MHD sodium alginate based Casson tetra hybrid nanofluid along with porous medium and two parallel plates

South African Journal of Chemical Engineering, Vol. 47 (2024), Iss. P.279

Optimized Overlapping Schwarz Waveform Relaxation for a Class of Time-Fractional Diffusion Problems

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Journal of Scientific Computing, Vol. 72 (2017), Iss. 2 P.842

Higher Order Computational Approach for Generalized Time-Fractional Diffusion Equation

Communications on Applied Mathematics and Computation, Vol. (2024), Iss.

A Highly Efficient Numerical Method for the Time-Fractional Diffusion Equation on Unbounded Domains

Journal of Scientific Computing, Vol. 99 (2024), Iss. 2

A Discretization Approach for the Nonlinear Fractional Logistic Equation

Entropy, Vol. 22 (2020), Iss. 11 P.1328

A finite difference scheme on graded meshes for time-fractional nonlinear Korteweg-de Vries equation

Applied Mathematics and Computation, Vol. 361 (2019), Iss. P.752

A fast compact finite difference method for quasilinear time fractional parabolic equation without singular kernel

International Journal of Computer Mathematics, Vol. 96 (2019), Iss. 7 P.1444

A QSC method for fractional subdiffusion equations with fractional boundary conditions and its application in parameters identification

Mathematics and Computers in Simulation, Vol. 174 (2020), Iss. P.153

Error analysis of a highly efficient and accurate temporal multiscale method for a fractional differential system

Chaos, Solitons & Fractals, Vol. 179 (2024), Iss. P.114447

On the phase separation in the ternary alloys: Numerical and computational simulations of the Atangana–Baleanu time‐fractional Cahn–Allen equation

Numerical Methods for Partial Differential Equations, Vol. 40 (2024), Iss. 2

A Fast Front-Tracking Approach and Its Analysis for a Temporal Multiscale Flow Problem with a Fractional Order Boundary Growth

SIAM Journal on Scientific Computing, Vol. 45 (2023), Iss. 5 P.B646

Numerical Solution of Fractional-Order Ordinary Differential Equations Using the Reformulated Infinite State Representation

Fractional Calculus and Applied Analysis, Vol. 22 (2019), Iss. 5 P.1321

Unconditional stability analysis of Grünwald Letnikov method for fractional-order delay differential equations

Chaos, Solitons & Fractals, Vol. 177 (2023), Iss. P.114193

Incomplete iterative solution of subdiffusion

Numerische Mathematik, Vol. 145 (2020), Iss. 3 P.693

Convergence analysis of the time-stepping numerical methods for time-fractional nonlinear subdiffusion equations

Fractional Calculus and Applied Analysis, Vol. 25 (2022), Iss. 2 P.453

Green's function for anisotropic dispersive poroelastic media based on the Radon transform and eigenvector diagonalization

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 475 (2019), Iss. 2221 P.20180610

Analyses of the Contour Integral Method for Time Fractional Normal-Subdiffusion Transport Equation

Journal of Scientific Computing, Vol. 97 (2023), Iss. 2

A RELIABLE APPROACH FOR ANALYSING THE NONLINEAR KDV EQUATION OF FRACTIONAL ORDER

Journal of Applied Analysis & Computation, Vol. 13 (2023), Iss. 3 P.1449

Wavelet-based Edge Multiscale Parareal Algorithm for subdiffusion equations with heterogeneous coefficients in a large time domain

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Journal of Computational and Applied Mathematics, Vol. 440 (2024), Iss. P.115608

The Laguerre-Hermite spectral methods for the time-fractional sub-diffusion equations on unbounded domains

Numerical Algorithms, Vol. 82 (2019), Iss. 4 P.1221

Numerical simulation for 2D/3D time fractional Maxwell’s system based on a fast second-order FDTD algorithm

Journal of Computational and Applied Mathematics, Vol. 416 (2022), Iss. P.114590

Conforming and nonconforming VEMs for the fourth-order reaction–subdiffusion equation: a unified framework

IMA Journal of Numerical Analysis, Vol. 42 (2022), Iss. 3 P.2238

Analysis of a Two-Phase MHD Free Convection Generalized Water–Ethylene Glycol (50 : 50) Dusty Brinkman-Type Nanofluid Pass through Microchannel

Journal of Mathematics, Vol. 2023 (2023), Iss. P.1

Fast High-Order Compact Finite Difference Methods Based on the Averaged L1 Formula for a Time-Fractional Mobile-Immobile Diffusion Problem

Journal of Scientific Computing, Vol. 99 (2024), Iss. 2

Strong error analysis of Euler methods for overdamped generalized Langevin equations with fractional noise: Nonlinear case

ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 57 (2023), Iss. 4 P.1981

Interpolated Coefficient Mixed Finite Elements for Semilinear Time Fractional Diffusion Equations

Fractal and Fractional, Vol. 7 (2023), Iss. 6 P.482

High-Order Schemes for Nonlinear Fractional Differential Equations

Fractal and Fractional, Vol. 6 (2022), Iss. 12 P.748

The Numerical Computation of the Time Fractional Schrödinger Equation on an Unbounded Domain

Computational Methods in Applied Mathematics, Vol. 18 (2018), Iss. 1 P.77

A Positivity-Preserving and Robust Fast Solver for Time-Fractional Convection–Diffusion Problems

Journal of Scientific Computing, Vol. 98 (2024), Iss. 3

New insight into the nano-fluid flow in a channel with tempered fractional operators

Nanotechnology, Vol. 35 (2024), Iss. 8 P.085403

Unconditional energy dissipation law and optimal error estimate of fast L1 schemes for a time-fractional Cahn–Hilliard problem

Communications in Nonlinear Science and Numerical Simulation, Vol. 124 (2023), Iss. P.107300

A New Class of Semi-Implicit Methods with Linear Complexity for Nonlinear Fractional Differential Equations

SIAM Journal on Scientific Computing, Vol. 40 (2018), Iss. 5 P.A2986

L3 approximation of Caputo derivative and its application to time-fractional wave equation-(I)

Mathematics and Computers in Simulation, Vol. 205 (2023), Iss. P.532

A high‐order and fast scheme with variable time steps for the time‐fractional Black‐Scholes equation

Mathematical Methods in the Applied Sciences, Vol. 46 (2023), Iss. 2 P.1990

Solving time-fractional differential equations via rational approximation

IMA Journal of Numerical Analysis, Vol. 43 (2023), Iss. 3 P.1263

Fitted schemes for Caputo-Hadamard fractional differential equations

Numerical Algorithms, Vol. 97 (2024), Iss. 1 P.135

An Energy Stable and Maximum Bound Preserving Scheme with Variable Time Steps for Time Fractional Allen--Cahn Equation

SIAM Journal on Scientific Computing, Vol. 43 (2021), Iss. 5 P.A3503

A parallel-in-time two-sided preconditioning for all-at-once system from a non-local evolutionary equation with weakly singular kernel

Journal of Computational Physics, Vol. 434 (2021), Iss. P.110221

Fractional Modeling of Non-Newtonian Casson Fluid between Two Parallel Plates

Journal of Mathematics, Vol. 2023 (2023), Iss. P.1

Müntz Spectral Methods for the Time-Fractional Diffusion Equation

Computational Methods in Applied Mathematics, Vol. 18 (2018), Iss. 1 P.43

Novel approximate solution for fractional differential equations by the optimal variational iteration method

Journal of Computational Science, Vol. 64 (2022), Iss. P.101841

Simple maximum principle preserving time-stepping methods for time-fractional Allen-Cahn equation

Advances in Computational Mathematics, Vol. 46 (2020), Iss. 2

An implicit difference scheme for time-fractional diffusion equations with a time-invariant type variable order

Applied Mathematics Letters, Vol. 120 (2021), Iss. P.107270

A lattice Boltzmann model for the fractional advection–diffusion equation coupled with incompressible Navier–Stokes equation

Applied Mathematics Letters, Vol. 101 (2020), Iss. P.106074

A fast compact difference scheme with unequal time-steps for the tempered time-fractional Black–Scholes model

International Journal of Computer Mathematics, Vol. 101 (2024), Iss. 9-10 P.989

Two-grid finite element method with an H2N2 interpolation for two-dimensional nonlinear fractional multi-term mixed sub-diffusion and diffusion wave equation

AIMS Mathematics, Vol. 9 (2024), Iss. 1 P.160

A fast finite difference/finite element method for the two-dimensional distributed-order time-space fractional reaction–diffusion equation

International Journal of Modeling, Simulation, and Scientific Computing, Vol. 11 (2020), Iss. 02 P.2050016

An Exponentially Convergent Scheme in Time for Time Fractional Diffusion Equations with Non-smooth Initial Data

Journal of Scientific Computing, Vol. 80 (2019), Iss. 2 P.717

A novel fast second order approach with high-order compact difference scheme and its analysis for the tempered fractional Burgers equation

Mathematics and Computers in Simulation, Vol. 227 (2025), Iss. P.168

Analysis of the anomalous diffusion in comb structure with absorbing boundary conditions

Journal of Computational Physics, Vol. 490 (2023), Iss. P.112315

Euler–Maruyama methods for Caputo tempered fractional stochastic differential equations

International Journal of Computer Mathematics, Vol. 101 (2024), Iss. 9-10 P.1113

Efficient hybrid group iterative methods in the solution of two-dimensional time fractional cable equation

Advances in Difference Equations, Vol. 2020 (2020), Iss. 1

Comparative Study of Dusty Tetra Hybrid Casson Nanofluid Flowing in a Generalized Two-Phase MHD Medium Between Parallel Microplates with a Porous Medium

The European Physical Journal Special Topics, Vol. 233 (2024), Iss. 13-14 P.2225

Dispersive long wave of nonlinear fractional Wu-Zhang system via a modified auxiliary equation method

AIP Advances, Vol. 9 (2019), Iss. 2

A Novel Numerical Method for Solving Nonlinear Fractional-Order Differential Equations and Its Applications

Fractal and Fractional, Vol. 8 (2024), Iss. 1 P.65

Stochastic Volterra integral equations with doubly singular kernels and their numerical solutions

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Communications in Nonlinear Science and Numerical Simulation, Vol. 116 (2023), Iss. P.106796

Generalized finite difference method with irregular mesh for a class of three-dimensional variable-order time-fractional advection-diffusion equations

Engineering Analysis with Boundary Elements, Vol. 132 (2021), Iss. P.345

Fast implicit difference schemes for time‐space fractional diffusion equations with the integral fractional Laplacian

Mathematical Methods in the Applied Sciences, Vol. 44 (2021), Iss. 1 P.441

Second-Order and Nonuniform Time-Stepping Schemes for Time Fractional Evolution Equations with Time–Space Dependent Coefficients

Journal of Scientific Computing, Vol. 89 (2021), Iss. 2

A second-order fitted scheme combined with time two-grid technique for two-dimensional nonlinear time fractional telegraph equations involving initial singularity

Journal of Computational and Applied Mathematics, Vol. 448 (2024), Iss. P.115936

A Symmetric Fractional-order Reduction Method for Direct Nonuniform Approximations of Semilinear Diffusion-wave Equations

Journal of Scientific Computing, Vol. 93 (2022), Iss. 1

Fast evaluation for the two-dimensional nonlinear coupled time–space fractional Klein–Gordon–Zakharov equations

Applied Mathematics Letters, Vol. 118 (2021), Iss. P.107148

A CG–DG method for Maxwell’s equations in Cole–Cole dispersive media

Journal of Computational and Applied Mathematics, Vol. 393 (2021), Iss. P.113480

A fast linearized numerical method for nonlinear time-fractional diffusion equations

Numerical Algorithms, Vol. 87 (2021), Iss. 1 P.381

An accurate and efficient space-time Galerkin spectral method for the subdiffusion equation

Science China Mathematics, Vol. 67 (2024), Iss. 10 P.2387

A fast time-stepping method based on the hp-version spectral collocation method for the nonlinear fractional delay differential equation

Communications in Nonlinear Science and Numerical Simulation, Vol. 126 (2023), Iss. P.107424

An H1 convergence of the spectral method for the time-fractional non-linear diffusion equations

Advances in Computational Mathematics, Vol. 47 (2021), Iss. 5

Sharp H1-norm error estimate of a cosine pseudo-spectral scheme for 2D reaction-subdiffusion equations

Numerical Algorithms, Vol. 83 (2020), Iss. 3 P.1223

Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations: A Second-Order Scheme

Communications in Computational Physics, Vol. 22 (2017), Iss. 4 P.1028

Highly Efficient and Energy Dissipative Schemes for the Time Fractional Allen--Cahn Equation

SIAM Journal on Scientific Computing, Vol. 43 (2021), Iss. 5 P.A3305

Fast high order difference schemes for the time fractional telegraph equation

Numerical Methods for Partial Differential Equations, Vol. 36 (2020), Iss. 1 P.154

A fast algorithm for two-dimensional distributed-order time-space fractional diffusion equations

Applied Mathematics and Computation, Vol. 425 (2022), Iss. P.127095

A fast difference scheme for the multi-term time fractional advection–diffusion equation with a non-linear source term

Chinese Journal of Physics, Vol. 89 (2024), Iss. P.86

L1-robust analysis of a fourth-order block-centered finite difference method for two-dimensional variable-coefficient time-fractional reaction-diffusion equations

Computers & Mathematics with Applications, Vol. 148 (2023), Iss. P.211

Accuracy and speed of splitting methods for three-dimensional space–time fractional diffusion equation withψ-Caputo derivatives

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Mathematics and Computers in Simulation, Vol. 188 (2021), Iss. P.226

Fast and Parallel Runge--Kutta Approximation of Fractional Evolution Equations

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SIAM Journal on Scientific Computing, Vol. 41 (2019), Iss. 2 P.A927

An Euler–Maruyama method for Caputo–Hadamard fractional stochastic differential equations on exponential meshes and its fast approximation

Numerical Algorithms, Vol. (2024), Iss.

A transformed $ L1 $ Legendre-Galerkin spectral method for time fractional Fokker-Planck equations

Networks and Heterogeneous Media, Vol. 18 (2023), Iss. 2 P.799

Exponential sum approximation for Mittag-Leffler function and its application to fractional Zener wave equation

Journal of Computational Physics, Vol. 410 (2020), Iss. P.109389

Numerical Analysis of the Nonuniform Fast L1 Formula for Nonlinear Time–Space Fractional Parabolic Equations

Journal of Scientific Computing, Vol. 95 (2023), Iss. 2

A fast finite volume method for spatial fractional diffusion equations on nonuniform meshes

Computers & Mathematics with Applications, Vol. 108 (2022), Iss. P.175

Convergence and superconvergence analysis for nonlinear delay reaction–diffusion system with nonconforming finite element

Numerical Methods for Partial Differential Equations, Vol. 39 (2023), Iss. 1 P.716

A fast implicit difference scheme for solving high-dimensional time-space fractional nonlinear Schrödinger equation

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International Journal of Computer Mathematics, Vol. 100 (2023), Iss. 7 P.1419

Enhanced parallel computation for time-fractional fluid dynamics: A fast time-stepping method with Newton-Krylov-Schwarz solver

Communications in Nonlinear Science and Numerical Simulation, Vol. 133 (2024), Iss. P.107952

Double fast algorithm for solving time-space fractional diffusion problems with spectral fractional Laplacian

Applied Mathematics and Computation, Vol. 475 (2024), Iss. P.128715

Two finite difference methods based on an H2N2 interpolation for two-dimensional time fractional mixed diffusion and diffusion-wave equations

Discrete & Continuous Dynamical Systems - B, Vol. 27 (2022), Iss. 2 P.1179

Fast $$\theta $$-Maruyama scheme for stochastic Volterra integral equations of convolution type: mean-square stability and strong convergence analysis

Computational and Applied Mathematics, Vol. 42 (2023), Iss. 3

The fast Euler-Maruyama method for solving multiterm Caputo fractional stochastic delay integro-differential equations

Numerical Algorithms, Vol. (2024), Iss.

A fast method and convergence analysis for the MHD flow model of generalized second-grade fluid

Computers & Mathematics with Applications, Vol. 171 (2024), Iss. P.175

Unconditionally optimal H1-norm error estimates of a fast and linearized Galerkin method for nonlinear subdiffusion equations

Computers & Mathematics with Applications, Vol. 107 (2022), Iss. P.70

A novel fast tempered algorithm with high-accuracy scheme for 2D tempered fractional reaction-advection-subdiffusion equation

Computers & Mathematics with Applications, Vol. 176 (2024), Iss. P.371

Numerical stability analysis of spatial-temporal fully discrete scheme for time-fractional delay Schrödinger equations

Numerical Algorithms, Vol. 97 (2024), Iss. 3 P.1237

Analysis of a fast element-free Galerkin method for the multi-term time-fractional diffusion equation

Mathematics and Computers in Simulation, Vol. 223 (2024), Iss. P.677

Fast Euler–Maruyama method for weakly singular stochastic Volterra integral equations with variable exponent

Numerical Algorithms, Vol. 92 (2023), Iss. 4 P.2433

A Weak Galerkin Finite Element Method for High Dimensional Time-fractional Diffusion Equation

Applied Mathematics and Computation, Vol. 386 (2020), Iss. P.125524

A fast Euler–Maruyama scheme and its strong convergence for multi-term Caputo tempered fractional stochastic differential equations

Communications in Nonlinear Science and Numerical Simulation, Vol. 138 (2024), Iss. P.108253

Some novel inequalities for Caputo Fabrizio fractional integrals involving (α,s)-convex functions with applications

Mathematical and Computer Modelling of Dynamical Systems, Vol. 30 (2024), Iss. 1 P.1

Convergence analysis of a fast second‐order time‐stepping numerical method for two‐dimensional nonlinear time–space fractional Schrödinger equation

Numerical Methods for Partial Differential Equations, Vol. 39 (2023), Iss. 1 P.657

α-robust analysis of fast and novel two-grid FEM with nonuniform L1 scheme for semilinear time-fractional variable coefficient diffusion equations

Tan, Zhijun

Communications in Nonlinear Science and Numerical Simulation, Vol. 131 (2024), Iss. P.107830

Fast difference scheme for a tempered fractional Burgers equation in porous media

Applied Mathematics Letters, Vol. 132 (2022), Iss. P.108143

Numerical analysis of Finite-Difference Time-Domain method for 2D/3D Maxwell's equations in a Cole-Cole dispersive medium

Computers & Mathematics with Applications, Vol. 93 (2021), Iss. P.230

An improved lattice Boltzmann model for variable-order time-fractional generalized Navier-Stokes equations with applications to permeability prediction

Chaos, Solitons & Fractals, Vol. 189 (2024), Iss. P.115616

Fast numerical scheme for the time-fractional option pricing model with asset-price-dependent variable order

Applied Numerical Mathematics, Vol. 192 (2023), Iss. P.414

A fast temporal second‐order difference scheme for the time‐fractional subdiffusion equation

Numerical Methods for Partial Differential Equations, Vol. 37 (2021), Iss. 3 P.1825

Time-fractional Allen–Cahn and Cahn–Hilliard phase-field models and their numerical investigation

Computers & Mathematics with Applications, Vol. 76 (2018), Iss. 8 P.1876

Legendre spectral methods based on two families of novel second-order numerical formulas for the fractional activator-inhibitor system

Applied Numerical Mathematics, Vol. 162 (2021), Iss. P.235

Time fractional model of free convection flow and dusty two‐phase couple stress fluid along vertical plates

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 103 (2023), Iss. 5

Numerical analysis for optimal quadratic spline collocation method in two space dimensions with application to nonlinear time-fractional diffusion equation

Advances in Computational Mathematics, Vol. 50 (2024), Iss. 2

Fast hybrid explicit group methods for solving 2D fractional advection-diffusion equation

AIMS Mathematics, Vol. 7 (2022), Iss. 9 P.15854

Superconvergence of Finite Element Approximations for the Fractional Diffusion-Wave Equation

Journal of Scientific Computing, Vol. 72 (2017), Iss. 3 P.917

A Spectrally Accurate Approximation to Subdiffusion Equations Using the Log Orthogonal Functions

SIAM Journal on Scientific Computing, Vol. 42 (2020), Iss. 2 P.A849

Numerical energy dissipation for time fractional volume-conserved Allen–Cahn model based on the ESAV and R-ESAV approaches

Communications in Nonlinear Science and Numerical Simulation, Vol. 137 (2024), Iss. P.108120

A fast fractional block-centered finite difference method for two-sided space-fractional diffusion equations on general nonuniform grids

Fractional Calculus and Applied Analysis, Vol. (2024), Iss.

Spectral solutions for the time-fractional heat differential equation through a novel unified sequence of Chebyshev polynomials

AIMS Mathematics, Vol. 9 (2023), Iss. 1 P.2137

Discrete Gradient Structure of a Second-Order Variable-Step Method for Nonlinear Integro-Differential Models

SIAM Journal on Numerical Analysis, Vol. 61 (2023), Iss. 5 P.2157

Recovery of the Order of Derivation for Fractional Diffusion Equations in an Unknown Medium

SIAM Journal on Applied Mathematics, Vol. 82 (2022), Iss. 3 P.1045

Efficient difference method for time-space fractional diffusion equation with Robin fractional derivative boundary condition

Numerical Algorithms, Vol. 88 (2021), Iss. 4 P.1965

A fast Galerkin finite element method for a space–time fractional Allen–Cahn equation

Journal of Computational and Applied Mathematics, Vol. 368 (2020), Iss. P.112482

Numerical algorithm for two-dimensional nonlinear Volterra-Fredholm integral equations and fractional integro-differential equations (of Hammerstein and mixed types)

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Engineering Computations, Vol. 38 (2021), Iss. 9 P.3548

Numerical Simulations of the Oscillating Second-Grade Fluid through a Rectangular Cross Duct with Fractional Constitution Relationship

Fractal and Fractional, Vol. 6 (2022), Iss. 11 P.666

A Parallel-in-Time Algorithm for High-Order BDF Methods for Diffusion and Subdiffusion Equations

SIAM Journal on Scientific Computing, Vol. 43 (2021), Iss. 6 P.A3627

Convergence and superconvergence analysis of finite element methods for nonlinear Ginzburg–Landau equation with Caputo derivative

Computational and Applied Mathematics, Vol. 42 (2023), Iss. 6

A priori and a posteriori error estimates of a space–time Petrov–Galerkin spectral method for time-fractional diffusion equation

Mathematics and Computers in Simulation, Vol. 219 (2024), Iss. P.559

A stable explicitly solvable numerical method for the Riesz fractional advection–dispersion equations

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Applied Mathematics and Computation, Vol. 332 (2018), Iss. P.209

On power law scaling dynamics for time-fractional phase field models during coarsening

Communications in Nonlinear Science and Numerical Simulation, Vol. 70 (2019), Iss. P.257

Analysis of a meshless generalized finite difference method for the time-fractional diffusion-wave equation

Computers & Mathematics with Applications, Vol. 172 (2024), Iss. P.134

Unconditionally Optimal Error Estimates of a Linearized Galerkin Method for Nonlinear Time Fractional Reaction–Subdiffusion Equations

Journal of Scientific Computing, Vol. 76 (2018), Iss. 2 P.848

Numerical simulation of the two-dimensional fractional Schrödinger equation for describing the quantum dynamics on a comb with the absorbing boundary conditions

Communications in Nonlinear Science and Numerical Simulation, Vol. 140 (2025), Iss. P.108407

A fast second-order predictor-corrector method for a nonlinear time-fractional Benjamin-Bona-Mahony-Burgers equation

Numerical Algorithms, Vol. 95 (2024), Iss. 2 P.693

A NONLOCAL STRUCTURAL DERIVATIVE MODEL BASED ON THE CAPUTO FRACTIONAL DERIVATIVE FOR SUPERFAST DIFFUSION IN HETEROGENEOUS MEDIA

Fractals, Vol. 28 (2020), Iss. 07 P.2050122

An integrated fractional partial differential equation and molecular dynamics model of anomalously diffusive transport in heterogeneous nano-pore structures

Journal of Computational Physics, Vol. 373 (2018), Iss. P.1000

An efficient and accurate method for modeling nonlinear fractional viscoelastic biomaterials

Computer Methods in Applied Mechanics and Engineering, Vol. 362 (2020), Iss. P.112834

A fast compact difference scheme on graded meshes for solving the time-fractional nonlinear KdV equation

International Journal of Computer Mathematics, Vol. (2024), Iss. P.1

Robust fast method for variable-order time-fractional diffusion equations without regularity assumptions of the true solutions

Applied Mathematics and Computation, Vol. 430 (2022), Iss. P.127273

A numerical method for two-dimensional multi-term time-space fractional nonlinear diffusion-wave equations

Applied Numerical Mathematics, Vol. 159 (2021), Iss. P.159

Midpoint-type integral inequalities for ( s , m )-convex functions in the third sense involving Caputo fractional derivatives and Caputo–Fabrizio integrals

Applied Mathematics in Science and Engineering, Vol. 32 (2024), Iss. 1

Optimal pointwise-in-time error analysis of a mixed finite element method for a multi-term time-fractional fourth-order equation

Computers & Mathematics with Applications, Vol. 135 (2023), Iss. P.149

Efficient Difference Schemes for the Caputo-Tempered Fractional Diffusion Equations Based on Polynomial Interpolation

Communications on Applied Mathematics and Computation, Vol. 3 (2021), Iss. 1 P.1

A Gauss–Jacobi Kernel Compression Scheme for Fractional Differential Equations

Baffet, Daniel

Journal of Scientific Computing, Vol. 79 (2019), Iss. 1 P.227

Numerical approximation and fast evaluation of the overdamped generalized Langevin equation with fractional noise

ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 54 (2020), Iss. 2 P.431

Numerical solutions of nonlinear fractional Wu–Zhang system for water surface versus three approximate schemes

Journal of Ocean Engineering and Science, Vol. 4 (2019), Iss. 2 P.144

Numerical schemes for modelling time-fractional dynamics of non-isothermal diffusion in soils

Bohaienko, V.O.

Mathematics and Computers in Simulation, Vol. 157 (2019), Iss. P.100

An α-robust fast algorithm for distributed-order time–space fractional diffusion equation with weakly singular solution

Mathematics and Computers in Simulation, Vol. 207 (2023), Iss. P.437

Energy stability of a temporal variable-step difference scheme for time-fractional nonlinear fourth-order reaction–diffusion equation

International Journal of Computer Mathematics, Vol. 100 (2023), Iss. 5 P.991

A fast Alikhanov algorithm with general nonuniform time steps for a two‐dimensional distributed‐order time–space fractional advection–dispersion equation

Numerical Methods for Partial Differential Equations, Vol. 39 (2023), Iss. 4 P.2885

Numerical learning approximation of time-fractional sub diffusion model on a semi-infinite domain

Chaos, Solitons & Fractals, Vol. 142 (2021), Iss. P.110435

A fast collocation approximation to a two-sided variable-order space-fractional diffusion equation and its analysis

Journal of Computational and Applied Mathematics, Vol. 388 (2021), Iss. P.113234

Efficient shifted fractional trapezoidal rule for subdiffusion problems with nonsmooth solutions on uniform meshes

BIT Numerical Mathematics, Vol. 62 (2022), Iss. 2 P.631

Superconvergence and Postprocessing of Collocation Methods for Fractional Differential Equations

Journal of Scientific Computing, Vol. 97 (2023), Iss. 2

A fast finite difference scheme for the time-space fractional diffusion equation

IFAC-PapersOnLine, Vol. 58 (2024), Iss. 12 P.174

Fast and efficient finite difference method for the distributed-order diffusion equation based on the staggered grids

Applied Numerical Mathematics, Vol. 174 (2022), Iss. P.34

An accurate and efficient algorithm for the time-fractional molecular beam epitaxy model with slope selection

Computer Physics Communications, Vol. 245 (2019), Iss. P.106842

Asymptotically Compatible Energy and Dissipation Law of the Nonuniform L2-$$1_{\sigma }$$ Scheme for Time Fractional Allen–Cahn Model

Journal of Scientific Computing, Vol. 99 (2024), Iss. 2

Numerical methods for fractional partial differential equations

International Journal of Computer Mathematics, Vol. 95 (2018), Iss. 6-7 P.1048

A Second Order Energy Dissipative Scheme for Time Fractional L$$^{2}$$ Gradient Flows using SAV Approach

Journal of Scientific Computing, Vol. 90 (2022), Iss. 1

Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan

Exponential Sum Approximations for t−β

McLean, William

2018

The Temporal Second Order Difference Schemes Based on the Interpolation Approximation for the Time Multi-term Fractional Wave Equation

Journal of Scientific Computing, Vol. 78 (2019), Iss. 1 P.467

Two-point stress–strain-rate correlation structure and non-local eddy viscosity in turbulent flows

Journal of Fluid Mechanics, Vol. 914 (2021), Iss.

Space-time finite element method for the distributed-order time fractional reaction diffusion equations

Applied Numerical Mathematics, Vol. 152 (2020), Iss. P.446

High accuracy error estimates of a Galerkin finite element method for nonlinear time fractional diffusion equation

Numerical Methods for Partial Differential Equations, Vol. 36 (2020), Iss. 2 P.284

Long time H1-stability of fast L2-1σ method on general nonuniform meshes for subdiffusion equations

Journal of Computational and Applied Mathematics, Vol. 440 (2024), Iss. P.115647

A second-order energy stable and nonuniform time-stepping scheme for time fractional Burgers' equation

Computers & Mathematics with Applications, Vol. 123 (2022), Iss. P.227

Error analyses on block‐centered finite difference schemes for distributed‐order non‐Fickian flow

Numerical Methods for Partial Differential Equations, Vol. 40 (2024), Iss. 3

CN ADI fast algorithm on non-uniform meshes for the three-dimensional nonlocal evolution equation with multi-memory kernels in viscoelastic dynamics

Applied Mathematics and Computation, Vol. 474 (2024), Iss. P.128680

Double weakly singular kernels in stochastic Volterra integral equations with application to the rough Heston model

Applied Mathematics and Computation, Vol. 475 (2024), Iss. P.128720

Two linearized schemes for time fractional nonlinear wave equations with fourth-order derivative

Journal of Applied Mathematics and Computing, Vol. 66 (2021), Iss. 1-2 P.561

A fast time integral finite difference method for a space-time fractional FitzHugh-Nagumo monodomain model in irregular domains

Journal of Computational Physics, Vol. 501 (2024), Iss. P.112744

Some Numerical Extrapolation Methods for the Fractional Sub-diffusion Equation and Fractional Wave Equation Based on the L1 Formula

Communications on Applied Mathematics and Computation, Vol. 4 (2022), Iss. 4 P.1313

FAST COMPACT DIFFERENCE SCHEME FOR THE FOURTH-ORDER TIME MULTI-TERM FRACTIONAL SUB-DIFFUSION EQUATIONS WITH THE FIRST DIRICHLET BOUNDARY

Journal of Applied Analysis & Computation, Vol. 11 (2021), Iss. 6 P.2736

Fast evaluation for magnetohydrodynamic flow and heat transfer of fractional Oldroyd‐B fluids between parallel plates

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 101 (2021), Iss. 10

Two-grid algorithms based on FEM for nonlinear time-fractional wave equations with variable coefficient

Computers & Mathematics with Applications, Vol. 143 (2023), Iss. P.119

Evolving Tangent Hyperbolic memristor based 6D chaotic model with fractional order derivative: Analysis and applications

Partial Differential Equations in Applied Mathematics, Vol. 7 (2023), Iss. P.100505

Mathematical analysis and numerical methods for Caputo-Hadamard fractional diffusion-wave equations

Applied Numerical Mathematics, Vol. 177 (2022), Iss. P.34

Efficient methods for nonlinear time fractional diffusion-wave equations and their fast implementations

Numerical Algorithms, Vol. 85 (2020), Iss. 2 P.375

Numerical Analysis of a Fast Finite Element Method for a Hidden-Memory Variable-Order Time-Fractional Diffusion Equation

Journal of Scientific Computing, Vol. 91 (2022), Iss. 2

A high-efficiency second-order numerical scheme for time-fractional phase field models by using extended SAV method

Nonlinear Dynamics, Vol. 102 (2020), Iss. 1 P.589

Two fast numerical methods for a generalized Oldroyd-B fluid model

Communications in Nonlinear Science and Numerical Simulation, Vol. 117 (2023), Iss. P.106963

A fast second‐order difference scheme for the space–time fractional equation

Numerical Methods for Partial Differential Equations, Vol. 35 (2019), Iss. 4 P.1326

Effective difference methods for solving the variable coefficient fourth-order fractional sub-diffusion equations

Networks and Heterogeneous Media, Vol. 18 (2022), Iss. 1 P.291

Computationally Efficient Hybrid Method for the Numerical Solution of the 2D Time Fractional Advection-Diffusion Equation

International Journal of Mathematical, Engineering and Management Sciences, Vol. 5 (2020), Iss. 3 P.432

An α-robust and new two-grid nonuniform L2-1 FEM for nonlinear time-fractional diffusion equation

Tan, Zhijun

Computers & Mathematics with Applications, Vol. 174 (2024), Iss. P.530

Robust and stable schemes for time fractional molecular beam epitaxial growth model using SAV approach

Journal of Computational Physics, Vol. 445 (2021), Iss. P.110628

Divide-and-Conquer Solver in Tensor-Train Format for d-Dimensional Time-Space Fractional Diffusion Equations

Journal of Scientific Computing, Vol. 96 (2023), Iss. 1

Analytical and numerical investigation on the tempered time-fractional operator with application to the Bloch equation and the two-layered problem

Nonlinear Dynamics, Vol. 109 (2022), Iss. 3 P.2041

Finite Element Formulation of Fractional Constitutive Laws Using the Reformulated Infinite State Representation

Fractal and Fractional, Vol. 5 (2021), Iss. 3 P.132

On Energy Dissipation Theory and Numerical Stability for Time-Fractional Phase-Field Equations

SIAM Journal on Scientific Computing, Vol. 41 (2019), Iss. 6 P.A3757

Waveform relaxation for fractional sub-diffusion equations

Numerical Algorithms, Vol. 87 (2021), Iss. 4 P.1445

Second-order non-uniform and fast two-grid finite element methods for non-linear time-fractional mobile/immobile equations with weak regularity

Tan, Zhijun

Applied Mathematics and Computation, Vol. 486 (2025), Iss. P.129043

Numerical blow-up analysis of the explicit L1-scheme for fractional ordinary differential equations

Numerical Algorithms, Vol. 89 (2022), Iss. 1 P.451

Temporal Second-Order Fast Finite Difference/Compact Difference Schemes for Time-Fractional Generalized Burgers’ Equations

Journal of Scientific Computing, Vol. 99 (2024), Iss. 2

Efficient Multistep Methods for Tempered Fractional Calculus: Algorithms and Simulations

SIAM Journal on Scientific Computing, Vol. 41 (2019), Iss. 4 P.A2510

Two-grid $ H^1 $-Galerkin mixed finite elements combined with $ L1 $ scheme for nonlinear time fractional parabolic equations

Electronic Research Archive, Vol. 31 (2023), Iss. 12 P.7207

All-at-once method for variable-order time fractional diffusion equations

Numerical Algorithms, Vol. 90 (2022), Iss. 1 P.31

An efficient quadratic finite volume method for variable coefficient Riesz space‐fractional diffusion equations

Mathematical Methods in the Applied Sciences, Vol. 44 (2021), Iss. 4 P.2934

The Exponential SAV Approach for the Time-Fractional Allen–Cahn and Cahn–Hilliard Phase-Field Models

Journal of Scientific Computing, Vol. 94 (2023), Iss. 2

A Review on Variable-Order Fractional Differential Equations: Mathematical Foundations, Physical Models, Numerical Methods and Applications

Fractional Calculus and Applied Analysis, Vol. 22 (2019), Iss. 1 P.27

A generalized magnetohydrodynamic two-phase free convection flow of dusty Casson fluid between parallel plates

Case Studies in Thermal Engineering, Vol. 29 (2022), Iss. P.101657

An H2N2 Interpolation for Caputo Derivative with Order in (1, 2) and Its Application to Time-Fractional Wave Equations in More Than One Space Dimension

Journal of Scientific Computing, Vol. 83 (2020), Iss. 2

Fast evaluation and high accuracy finite element approximation for the time fractional subdiffusion equation

Numerical Methods for Partial Differential Equations, Vol. 34 (2018), Iss. 2 P.705

3-D Forward Modeling of Transient EM Field in Rough Media Using Implicit Time-Domain Finite-Element Method

IEEE Transactions on Geoscience and Remote Sensing, Vol. 61 (2023), Iss. P.1

Galerkin finite element method for a two-dimensional tempered time–space fractional diffusion equation with application to a Bloch–Torrey equation retaining Larmor precession

Mathematics and Computers in Simulation, Vol. 206 (2023), Iss. P.517

On the recurrent computation of fractional operator with Mittag-Leffler kernel

Bohaienko, Vsevolod

Applied Numerical Mathematics, Vol. 162 (2021), Iss. P.137

A second-order and nonuniform time-stepping maximum-principle preserving scheme for time-fractional Allen-Cahn equations

Journal of Computational Physics, Vol. 414 (2020), Iss. P.109473

A fast temporal second-order compact ADI difference scheme for the 2D multi-term fractional wave equation

Numerical Algorithms, Vol. 86 (2021), Iss. 2 P.761

Fast algorithm based on TT-M FE system for space fractional Allen–Cahn equations with smooth and non-smooth solutions

Journal of Computational Physics, Vol. 379 (2019), Iss. P.351

Unconditionally convergent and superconvergent FEMs for nonlinear coupled time-fractional prey–predator problem

Computational and Applied Mathematics, Vol. 42 (2023), Iss. 3

Two Finite Difference Schemes for Multi-Dimensional Fractional Wave Equations with Weakly Singular Solutions

Computational Methods in Applied Mathematics, Vol. 21 (2021), Iss. 4 P.913

Stable numerical schemes for time-fractional diffusion equation with generalized memory kernel

Applied Numerical Mathematics, Vol. 172 (2022), Iss. P.546

Numerical calculation and fast method for the magnetohydrodynamic flow and heat transfer of fractional Jeffrey fluid on a two-dimensional irregular convex domain

Computers & Mathematics with Applications, Vol. 151 (2023), Iss. P.473

High order numerical methods based on quadratic spline collocation method and averaged L1 scheme for the variable-order time fractional mobile/immobile diffusion equation

Computers & Mathematics with Applications, Vol. 171 (2024), Iss. P.82

New explicit and accelerated techniques for solving fractional order differential equations

Applied Mathematics and Computation, Vol. 379 (2020), Iss. P.125228

A superlinear numerical scheme for multi-term fractional nonlinear ordinary differential equations

International Journal of Modeling, Simulation, and Scientific Computing, Vol. 11 (2020), Iss. 02 P.2050015

Fast algorithm for nonlocal Allen–Cahn equation with scalar auxiliary variable approach

Applied Mathematics Letters, Vol. 126 (2022), Iss. P.107805

An efficient FDTD algorithm for 2D/3D time fractional Maxwell’s system

Applied Mathematics Letters, Vol. 116 (2021), Iss. P.106992

A Fast High Order Method for the Time-Fractional Diffusion Equation

SIAM Journal on Numerical Analysis, Vol. 57 (2019), Iss. 6 P.2829

A class of efficient time-stepping methods for multi-term time-fractional reaction-diffusion-wave equations

Applied Numerical Mathematics, Vol. 165 (2021), Iss. P.56

Lattice BGK model for time-fractional incompressible Navier–Stokes equations

Applied Mathematics Letters, Vol. 114 (2021), Iss. P.106911

A parallel-in-time iterative algorithm for Volterra partial integro-differential problems with weakly singular kernel

Journal of Computational Physics, Vol. 417 (2020), Iss. P.109576

A Fast and Efficient Method for 3-D Transient Electromagnetic Modeling Considering IP Effect

IEEE Transactions on Geoscience and Remote Sensing, Vol. 62 (2024), Iss. P.1

Exponential-sum-approximation technique for variable-order time-fractional diffusion equations

Journal of Applied Mathematics and Computing, Vol. 68 (2022), Iss. 1 P.323

A Parareal Finite Volume Method for Variable-Order Time-Fractional Diffusion Equations

Journal of Scientific Computing, Vol. 85 (2020), Iss. 1

A bilateral preconditioning for an L2-type all-at-once system from time-space non-local evolution equations with a weakly singular kernel

Computers & Mathematics with Applications, Vol. 148 (2023), Iss. P.200

α-Robust H1-norm analysis of a finite element method for the superdiffusion equation with weak singularity solutions

Computers & Mathematics with Applications, Vol. 118 (2022), Iss. P.159

Exploring the potential of heat transfer and entropy generation of generalized dusty tetra hybrid nanofluid in a microchannel

Chinese Journal of Physics, Vol. 89 (2024), Iss. P.1009

Parallel finite-difference algorithms for three-dimensional space-fractional diffusion equation with $$\psi $$-Caputo derivatives

Bohaienko, V. O.

Computational and Applied Mathematics, Vol. 39 (2020), Iss. 3

A fast finite volume method for conservative space–time fractional diffusion equations discretized on space–time locally refined meshes

Computers & Mathematics with Applications, Vol. 78 (2019), Iss. 5 P.1345

Mathematical and Physical Analysis of Fractional Estevez–Mansfield–Clarkson Equation

Fractal and Fractional, Vol. 8 (2024), Iss. 8 P.467

Lattice Boltzmann model for incompressible flows through porous media with time-fractional effects

Communications in Nonlinear Science and Numerical Simulation, Vol. 135 (2024), Iss. P.108035

Second‐order difference scheme for the time fractional mixed diffusion‐wave equation with initial weak regularity

Mathematical Methods in the Applied Sciences, Vol. (2023), Iss.

A superlinear convergence scheme for nonlinear fractional differential equations and its fast implement

International Journal of Modeling, Simulation, and Scientific Computing, Vol. 10 (2019), Iss. 01 P.1941001

Efficient numerical method for multi-term time-fractional diffusion equations with Caputo-Fabrizio derivatives

Fan, Bin

AIMS Mathematics, Vol. 9 (2024), Iss. 3 P.7293

Exploration of generalized two-phase free convection magnetohydrodynamic flow of dusty tetra-hybrid Casson nanofluid between parallel microplates

Nanotechnology Reviews, Vol. 12 (2023), Iss. 1

A fast algorithm for time-fractional diffusion equation with space-time-dependent variable order

Numerical Algorithms, Vol. 94 (2023), Iss. 4 P.1705

Energy stability and convergence of variable-step L1 scheme for the time fractional Swift-Hohenberg model

Fractional Calculus and Applied Analysis, Vol. 27 (2024), Iss. 1 P.82

Approximate Solution of a Kind of Time-Fractional Evolution Equations Based on Fast L1 Formula and Barycentric Lagrange Interpolation

Fractal and Fractional, Vol. 8 (2024), Iss. 11 P.675

Fast Crank-Nicolson compact difference scheme for the two-dimensional time-fractional mobile/immobile transport equation

AIMS Mathematics, Vol. 6 (2021), Iss. 6 P.6242

An Efficient Parallel Approximate Algorithm for Solving Time Fractional Reaction-Diffusion Equations

Mathematical Problems in Engineering, Vol. 2020 (2020), Iss. P.1

Mathematical analysis of Ebola considering transmission at treatment centres and survivor relapse using fractal-fractional Caputo derivatives in Uganda

Mathematical Modelling and Numerical Simulation with Applications, Vol. 4 (2024), Iss. 3 P.296

Fast solvers for finite difference scheme of two-dimensional time-space fractional differential equations

Numerical Algorithms, Vol. 84 (2020), Iss. 1 P.37

Error estimate of the fast L1 method for time-fractional subdiffusion equations

Applied Mathematics Letters, Vol. 133 (2022), Iss. P.108288

Convergence and stability of compact finite difference method for nonlinear time fractional reaction–diffusion equations with delay

Applied Mathematics and Computation, Vol. 337 (2018), Iss. P.144

A fast difference scheme for the variable coefficient time-fractional diffusion wave equations

Applied Numerical Mathematics, Vol. 167 (2021), Iss. P.31

A Fast Compact Finite Difference Method for Fractional Cattaneo Equation Based on Caputo–Fabrizio Derivative

Mathematical Problems in Engineering, Vol. 2020 (2020), Iss. P.1

A Fast High-Order Predictor–Corrector Method on Graded Meshes for Solving Fractional Differential Equations

Fractal and Fractional, Vol. 6 (2022), Iss. 9 P.516

Temporal second-order fully discrete two-grid methods for nonlinear time-fractional variable coefficient diffusion-wave equations

Applied Mathematics and Computation, Vol. 466 (2024), Iss. P.128457

Numerical Solution of the Time-Fractional Sub-Diffusion Equation on an Unbounded Domain in Two-Dimensional Space

East Asian Journal on Applied Mathematics, Vol. 7 (2017), Iss. 3 P.439

Compressing the memory variables in constant-Q viscoelastic wave propagation via an improved sum-of-exponentials approximation

Journal of Computational Physics, Vol. 518 (2024), Iss. P.113326

A weighted ADI scheme with variable time steps for diffusion-wave equations

Calcolo, Vol. 60 (2023), Iss. 4

A Hidden-Memory Variable-Order Time-Fractional Optimal Control Model: Analysis and Approximation

SIAM Journal on Control and Optimization, Vol. 59 (2021), Iss. 3 P.1851

Good (and Not So Good) Practices in Computational Methods for Fractional Calculus

Mathematics, Vol. 8 (2020), Iss. 3 P.324

Magnetohydrodynamics flow and heat transfer of novel generalized Kelvin–Voigt viscoelastic nanofluids over a moving plate

Physics of Fluids, Vol. 36 (2024), Iss. 6

An efficient numerical method on modified space-time sparse grid for time-fractional diffusion equation with nonsmooth data

Numerical Algorithms, Vol. 94 (2023), Iss. 4 P.1561

A Family of Transformed Difference Schemes for Nonlinear Time-Fractional Equations

Fractal and Fractional, Vol. 7 (2023), Iss. 1 P.96

A fast linearized finite difference method for the nonlinear multi-term time-fractional wave equation

Applied Numerical Mathematics, Vol. 151 (2020), Iss. P.448

A preconditioned fast finite element approximation to variable-order time-fractional diffusion equations in multiple space dimensions

Applied Numerical Mathematics, Vol. 163 (2021), Iss. P.15

An implicit difference scheme and algorithm implementation for the one-dimensional time-fractional Burgers equations

Mathematics and Computers in Simulation, Vol. 166 (2019), Iss. P.298

Roundoff error problems in interpolation methods for time-fractional problems

Applied Numerical Mathematics, Vol. 203 (2024), Iss. P.202

A fast compact finite difference scheme for the fourth-order diffusion-wave equation

International Journal of Computer Mathematics, Vol. 101 (2024), Iss. 2 P.170

Fractional modeling and analysis of unsteady squeezing flow of Casson nanofluid via extended He-Laplace algorithm in Liouville-Caputo sense

Alexandria Engineering Journal, Vol. 73 (2023), Iss. P.579

Variable-step numerical schemes and energy dissipation laws for time fractional Cahn–Hilliard model

Applied Mathematics Letters, Vol. 149 (2024), Iss. P.108929

Error analysis of fast L1 ADI finite difference/compact difference schemes for the fractional telegraph equation in three dimensions

Mathematics and Computers in Simulation, Vol. 205 (2023), Iss. P.205

Using hierarchical matrices in the solution of the time-fractional heat equation by multigrid waveform relaxation

Journal of Computational Physics, Vol. 416 (2020), Iss. P.109540

Computational Insights into the Unstable Fixed Point of the Fractional Difference Logistic Map

Mathematics, Vol. 12 (2024), Iss. 23 P.3635

An efficient second order stabilized scheme for the two dimensional time fractional Allen-Cahn equation

Applied Numerical Mathematics, Vol. 165 (2021), Iss. P.216

An L1 Legendre–Galerkin spectral method with fast algorithm for the two-dimensional nonlinear coupled time fractional Schrödinger equation and its parameter estimation

Computers & Mathematics with Applications, Vol. 82 (2021), Iss. P.13

Analysis and numerical solution of a nonlinear variable-order fractional differential equation

Advances in Computational Mathematics, Vol. 45 (2019), Iss. 5-6 P.2647

A fast parallel difference method for solving the non-homogeneous time-fractional Schrödinger equation

International Conference on Artificial Intelligence, Automation and High Performance Computing, (2024), P.408

A novel method for state of health estimation of lithium-ion batteries based on fractional-order differential voltage-capacity curve

Applied Energy, Vol. 377 (2025), Iss. P.124404

A Corrected L1 Method for a Time-Fractional Subdiffusion Equation

Journal of Scientific Computing, Vol. 95 (2023), Iss. 3

Wave propagation in poroviscoelastic vertical transversely isotropic media: A sum-of-exponentials approximation for the simulation of fractional Biot-squirt equations

GEOPHYSICS, Vol. 90 (2025), Iss. 1 P.T1

Exploring the couple stress flow of sodium alginate-based casson tetra hybrid nanofluid between inclined parallel microplates using Fourier analysis and Fick's laws

Materials Today Communications, Vol. 38 (2024), Iss. P.107677

A Generalized Two‐Phase Free Convection Flow of Dusty Jeffrey Fluid between Infinite Vertical Parallel Plates with Heat Transfer

Journal of Mathematics, Vol. 2022 (2022), Iss. 1

A novel explicit fast numerical scheme for the Cauchy problem for integro-differential equations with a difference kernel and its application

Computers & Mathematics with Applications, Vol. 175 (2024), Iss. P.330

Efficient Preconditioning for Time Fractional Diffusion Inverse Source Problems

SIAM Journal on Matrix Analysis and Applications, Vol. 41 (2020), Iss. 4 P.1857

An accurate spectral method for the transverse magnetic mode of Maxwell equations in Cole-Cole dispersive media

Advances in Computational Mathematics, Vol. 45 (2019), Iss. 2 P.707

Analysis of a Time-Fractional Substantial Diffusion Equation of Variable Order

Fractal and Fractional, Vol. 6 (2022), Iss. 2 P.114

A multi-time-scale wall model for large-eddy simulations and applications to non-equilibrium channel flows

Journal of Fluid Mechanics, Vol. 974 (2023), Iss.

A Legendre spectral method on graded meshes for the two-dimensional multi-term time-fractional diffusion equation with non-smooth solutions

Applied Mathematics Letters, Vol. 104 (2020), Iss. P.106247

Linearized transformed L1 finite element methods for semi-linear time-fractional parabolic problems

Applied Mathematics and Computation, Vol. 458 (2023), Iss. P.128242

A single-sided all-at-once preconditioning for linear system from a non-local evolutionary equation with weakly singular kernels

Computers & Mathematics with Applications, Vol. 169 (2024), Iss. P.1

A fast numerical scheme for a variably distributed-order time-fractional diffusion equation and its analysis

Computers & Mathematics with Applications, Vol. 108 (2022), Iss. P.24

Approximate solution of the Cauchy problem for a first-order integrodifferential equation with solution derivative memory

Vabishchevich, P.N.

Journal of Computational and Applied Mathematics, Vol. 422 (2023), Iss. P.114887

Unconditional convergence analysis of two linearized Galerkin FEMs for the nonlinear time-fractional diffusion-wave equation

Results in Applied Mathematics, Vol. 19 (2023), Iss. P.100389

An Euler–Maruyama method and its fast implementation for multiterm fractional stochastic differential equations

Mathematical Methods in the Applied Sciences, Vol. 46 (2023), Iss. 2 P.1556

Time two-grid technique combined with temporal second order difference method for two-dimensional semilinear fractional sub-diffusion equations

Applied Mathematics Letters, Vol. 129 (2022), Iss. P.107919

Several effective algorithms for nonlinear time fractional models

Applied Mathematics and Computation, Vol. 363 (2019), Iss. P.124598

Fast difference scheme for the reaction-diffusion-advection equation with exact artificial boundary conditions

Applied Numerical Mathematics, Vol. 173 (2022), Iss. P.395

LDG schemes with second order implicit time discretization for a fractional sub-diffusion equation

Results in Applied Mathematics, Vol. 4 (2019), Iss. P.100079

Variable-step L1 method combined with time two-grid algorithm for multi-singularity problems arising from two-dimensional nonlinear delay fractional equations

Communications in Nonlinear Science and Numerical Simulation, Vol. 139 (2024), Iss. P.108270

Backward Diffusion-Wave Problem: Stability, Regularization, and Approximation

SIAM Journal on Scientific Computing, Vol. 44 (2022), Iss. 5 P.A3183