A modified Euler-Maruyama method for Riemann-Liouville stochastic fractional integro-differential equations

In this paper, we propose a modified Euler-Maruyama (EM) method for Riemann-Liouville stochastic fractional integro-differential equations with weakly singular kernels, and then analyse the strong convergence of the proposed EM method. Specifically, we transform the considered stochastic fractional integro-differential equation into its equivalent form of stochastic Volterra integral equations and derive the corresponding modified EM method. Then, the strong convergence 1 - alpha order of the proposed method is established, where alpha is the order of Riemann-Liouville fractional derivative with 0<alpha<1. Finally, numerical experiments are demonstrated to support our theoretical results.