Existence results for some fractional stochastic integro-differential equations via measures of non-compactness

Abstract

Using fixed point theorems is one method used to prove the existence of solutions in many types of integral equations. This study focuses on applying a generalization of Petryshyn's fixed point theorem to solve a general form of fractional stochastic integro-differential equations in the Banach algebra C(Ia). Besides stating and proving the relevant theorem, the reasons for the superiority of the new method compared some similar methods, were explained. In addition, to confirm the efficiency and check the validity of results, a part of the paper dedicated to solving some stochastic integral equations.