A Galerkin finite element method for time-fractional stochastic heat equation

Abstract

In this study, a Galerkin finite element method is presented for time-fractional stochastic heat equation driven by multiplicative noise, which arises from the consideration of heat transport in porous media with thermal memory with random effects. The spatial and temporal regularity properties of mild solution to the given problem under certain sufficient conditions are obtained. Numerical techniques are developed by the standard Galerkin finite element method in spatial direction, and Gorenflo-Mainardi-Moretti-Paradisi scheme is applied in temporal direction. The convergence error estimates for both semi-discrete and fully discrete schemes are established. Finally, numerical example is provided to verify the theoretical results.

An inverse random source problem in a stochastic fractional diffusion equation

“…Time fractional stochastic PDEs have gained attention recently, see e.g. [14,44,37,48] and references therein. Our setup differs slightly from these works: previous studies often assume some spatial randomness of the source, whereas our source term is random only in time.…”

Well‐posedness of time‐space fractional stochastic evolution equations driven by α‐stable noise

“…Gorenflo‐Mainardi‐Moretti‐Paradisi (GMMP) scheme) is adapted to approximate the time‐fractional derivatives, and finite difference method is used to discrete the space direction. Figures A, A, and A show the numerical results of the corresponding deterministic problem ( ) obtained by numerical scheme when we take η = 0.5,0.8,1.0, respectively.…”

Caratheodory’s approximation for a type of Caputo fractional stochastic differential equations

“…Its worth mentioning that the Euler-Maruyama type approximate results for Caputo fractional stochastic differential equations have been established by [17]. For more related work, see [12,[18][19][20][21][22].…”