Numerical Simulation for the Variable-Order Fractional Schrödinger Equation with the Quantum Riesz-Feller Derivative
Year: 2017
Author: N. H. Sweilam, M. M. Abou Hasan
Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 4 : pp. 990–1011
Abstract
In this paper the space variable-order fractional Schrödinger equation (VOFSE) is studied numerically, where the variable-order fractional derivative is described here in the sense of the quantum Riesz-Feller definition. The proposed numerical method is the weighted average non-standard finite difference method (WANSFDM). Special attention is given to study the stability analysis and the convergence of the proposed method. Finally, two numerical examples are provided to show that this method is reliable and computationally efficient.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2015.m1312
Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 4 : pp. 990–1011
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Variable-order Schrödinger equation quantum Riesz-Feller variable-order definition weighted average non-standard finite difference method Jon von Neumann stability analysis.
Author Details
-
On variable‐order Salmonella bacterial infection mathematical model
Sweilam, Nasser H. | Abou Hasan, Muner M. | Al‐ Mekhlafi, Seham M.Mathematical Methods in the Applied Sciences, Vol. 47 (2024), Iss. 5 P.3443
https://doi.org/10.1002/mma.8548 [Citations: 8] -
Numerical study for a novel variable-order multiple time delay awareness programs mathematical model
Sweilam, Nasser | AL-Mekhlafi, Seham | Shatta, Salma | Baleanu, DumitruApplied Numerical Mathematics, Vol. 158 (2020), Iss. P.212
https://doi.org/10.1016/j.apnum.2020.07.016 [Citations: 5] -
Time fractional of nonlinear heat-wave propagation in a rigid thermal conductor: Numerical treatment
Sweilam, N.H. | Abou Hasan, M.M. | Al-Mekhlafi, S.M. | Alkhatib, S.A.Alexandria Engineering Journal, Vol. 61 (2022), Iss. 12 P.10153
https://doi.org/10.1016/j.aej.2022.03.034 [Citations: 6] -
Numerical solutions of a general coupled nonlinear system of parabolic and hyperbolic equations of thermoelasticity
Sweilam, N. H. | Abou Hasan, M. M.The European Physical Journal Plus, Vol. 132 (2017), Iss. 5
https://doi.org/10.1140/epjp/i2017-11484-x [Citations: 14] -
A novel variable‐order fractional nonlinear Klein Gordon model: A numerical approach
Sweilam, Nasser H. | Al‐Mekhlafi, Seham M. | Albalawi, Anan O.Numerical Methods for Partial Differential Equations, Vol. 35 (2019), Iss. 5 P.1617
https://doi.org/10.1002/num.22367 [Citations: 13] -
Variable order fractional diabetes models: numerical treatment
Abou Hasan, Muner M.
International Journal of Modelling and Simulation, Vol. (2024), Iss. P.1
https://doi.org/10.1080/02286203.2024.2349508 [Citations: 0] -
Time-space variable-order fractional nonlinear system of thermoelasticity: numerical treatment
Assiri, Taghreed A.
Advances in Difference Equations, Vol. 2020 (2020), Iss. 1
https://doi.org/10.1186/s13662-020-02740-8 [Citations: 2] -
Optimal control of variable-order fractional model for delay cancer treatments
Sweilam, N.H. | AL-Mekhlafi, S.M. | Albalawi, A.O. | Tenreiro Machado, J.A.Applied Mathematical Modelling, Vol. 89 (2021), Iss. P.1557
https://doi.org/10.1016/j.apm.2020.08.012 [Citations: 43] -
Approximation of the Fractional Variable Order Wave Model by Weighted Average Finite Difference Method
Assiri, Taghreed A. | Alsulami, Saja A.Journal of Computational and Theoretical Nanoscience, Vol. 18 (2021), Iss. 6 P.1685
https://doi.org/10.1166/jctn.2021.9730 [Citations: 0] -
New studies for general fractional financial models of awareness and trial advertising decisions
Sweilam, Nasser H. | Abou Hasan, Muner M. | Baleanu, DumitruChaos, Solitons & Fractals, Vol. 104 (2017), Iss. P.772
https://doi.org/10.1016/j.chaos.2017.09.013 [Citations: 54] -
Fractional paradigms in quantum chemistry
Mostafanejad, Mohammad
International Journal of Quantum Chemistry, Vol. 121 (2021), Iss. 20
https://doi.org/10.1002/qua.26762 [Citations: 3] -
A Fourth-Order Compact Finite Difference Scheme for Solving the Time Fractional Carbon Nanotubes Model
Sweilam, N. H. | Khater, Khloud R. | Asker, Zafer M. | Kareem, Waleed Abdel | Bellucci, StefanoThe Scientific World Journal, Vol. 2022 (2022), Iss. P.1
https://doi.org/10.1155/2022/1426837 [Citations: 1] -
Laboratory Testing and Modeling of Creep Deformation for Sandstone Including Initial Temperature Damage
Liu, Xiaolin | Li, Dejian | Li, ChunxiaoRock Mechanics and Rock Engineering, Vol. 56 (2023), Iss. 4 P.2479
https://doi.org/10.1007/s00603-022-03204-z [Citations: 5] -
Propagation and interaction between special fractional soliton and soliton molecules in the inhomogeneous fiber
Wu, Gang-Zhou | Dai, Chao-Qing | Wang, Yue-Yue | Chen, Yi-XiangJournal of Advanced Research, Vol. 36 (2022), Iss. P.63
https://doi.org/10.1016/j.jare.2021.05.004 [Citations: 13] -
An Improved Method for Nonlinear Variable-Order Lévy–Feller Advection–Dispersion Equation
Sweilam, N. H. | Hasan, M. M. AbouBulletin of the Malaysian Mathematical Sciences Society, Vol. 42 (2019), Iss. 6 P.3021
https://doi.org/10.1007/s40840-018-0644-7 [Citations: 11] -
Optimal control problem of variable-order delay system of advertising procedure: Numerical treatment
Sweilam, Nasser H. | Assiri, Taghreed A. | Hasan, Muner M. AbouDiscrete & Continuous Dynamical Systems - S, Vol. 15 (2022), Iss. 5 P.1247
https://doi.org/10.3934/dcdss.2021085 [Citations: 9]