The Convergence of Euler-Maruyama Method of Differential Equations

In this paper, we first prove the existence and uniqueness theorem of the solution of nonlinear variable-order fractional stochastic differential equations (VFS-DEs). We futher constructe the Euler-Maruyama method to solve the equations and prove the convergence in mean and the strong convergence of the method. In par-ticular, when the fractional order is no longer varying, the conclusions obtained are consistent with the relevant conclusions in the existing literature. Finally, the numeri-cal experiments at the end of the article verify the correctness of the theoretical results obtained.