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

Abstract

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 order of the proposed method is established, where α is the order of Riemann–Liouville fractional derivative with . Finally, numerical experiments are demonstrated to support our theoretical results.