Analyzing the continuity of the mild solution in finite element analysis of semilinear stochastic subdiffusion problems

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.