Analyzing the continuity of the mild solution in finite element analysis of semilinear stochastic subdiffusion problems
- Resource Type
- article
- Authors
- Fang Cheng; Ye Hu; Mati ur Rahman
- Source
- AIMS Mathematics, Vol 9, Iss 4, Pp 9364-9379 (2024)
- Subject
- stochastic time-fractional equation
nonsmooth data analysis
continuity
error estimate
Mathematics
QA1-939
- Language
- English
- ISSN
- 2473-6988
This paper aimed to further introduce the finite element analysis of non-smooth data for semilinear stochastic subdiffusion problems driven by fractionally integrated additive noise. The mild solution of this stochastic model consisted of three different Mittag-Leffler functions. We analyzed the smoothness of the solution and utilized complex integration to approximate the error of the solution operator under non-smooth data. Consequently, optimal convergence estimates were obtained, and we also obtained the continuity conditions of the mild solution. Finally, the influence of the fractional parameters $ \alpha $ and $ \gamma $ on the convergence rates were accurately demonstrated through numerical examples.