Approximation of Solutions to Stochastic Fractional Integro-Differential Equation with Deviated Argument

Abstract

In this paper, we study a stochastic fractional integro-differential equation with deviated argument in a separable Hilbert space. We used the semigroup theory of linear operators to study the existence, uniqueness and convergence of approximate solutions to the given equation with the help of stochastic version of the well-known Banach fixed point theorem. Moreover, the convergence of Faedo–Galerkin approximation of the solution is shown. In the last, we give an example to illustrate the applications of the abstract results.