@article{Cheng2024, 
author = {Fang Cheng and Ye Hu and Mati ur Rahman},
title = {Analyzing the continuity of the mild solution in finite element analysis of semilinear stochastic subdiffusion problems},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {4},
pages = {9364-9379},
keywords = {stochastic time-fractional equation, nonsmooth data analysis, continuity, error estimate},
url = {https://www.sciopen.com/article/10.3934/math.2024456},
doi = {10.3934/math.2024456},
abstract = {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    α and    γ on the convergence rates were accurately demonstrated through numerical examples.}
}