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

TL;DR

This paper investigates the existence of solutions for a complex class of fractional nonlocal neutral stochastic differential equations with impulses and delays, incorporating jumps and noise in Hilbert spaces, using fixed point theorems.

Contribution

It introduces a new existence result for fractional nonlocal neutral stochastic differential equations with non-instantaneous impulses and state-dependent delays, without requiring compactness of resolvent operators.

Findings

Established existence of mild solutions using fixed point theorem.

Developed theoretical framework for equations with non-instantaneous impulses and delays.

Provided an example to illustrate the theoretical results.

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.