Existence of the Mild Solution for an Impulsive Nonlocal Neutral Stochastic Fractional Differential Inclusions with Infinite Delay

Abstract

This paper studies an impulsive nonlocal neutral stochastic fractional integro-differential inclusions with infinite delays in an arbitrary separable Hilbert space X. The sufficient conditions proving the existence of mild solution of the nonlocal stochastic inclusion problem with impulsive conditions are derived by using resolvent operator and fixed point theorem for multi-valued operators due to O’Regan. An example is also presented to illustrate the obtained theory.