Existence of Fractional Nonlocal Neutral Stochastic Differential Equation of Order 1 < q < 2 with Non-instantaneous Impulses and State-Dependent Delay

Abstract

This article addresses a new class of fractional nonlocal neutral stochastic differential system of order 1<q<2 including non-instantaneous impulses(NIIs) and state-dependent delay(SDD) with the Poisson jumps and the Wiener process in Hilbert spaces. We examine the existence of a mild solution without assuming the compactness of the resolvent operators. The Monch fixed point theorem is used along with the Hausdorff measure of noncompactness. An example is constructed to verify the theoretical developments.