Year: 2025
Author: Mariam Al-Maskari
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 3 : pp. 569–587
Abstract
This paper investigates a semilinear stochastic fractional Rayleigh-Stokes equation featuring a Riemann-Liouville fractional derivative of order $α ∈ (0, 1)$ in time and a fractional time-integral noise. The study begins with an examination of the solution’s existence, uniqueness, and regularity. The spatial discretization is then carried out using a finite element method, and the error estimate is analyzed. A convolution quadrature method generated by the backward Euler method is employed for the time discretization resulting in a fully discrete scheme. The error estimate for the fully discrete solution is considered based on the regularity of the solution, and a strong convergence rate is established. The paper concludes with numerical tests to validate the theoretical findings.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2311-m2023-0047
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 3 : pp. 569–587
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Riemann-Liouville fractional derivative Stochastic Rayleigh-Stokes equation Finite element method Convolution quadrature Error estimates.