Infinite delay fractional stochastic integro-differential equations with Poisson jumps of neutral type

Abstract

This paper addresses the study of nonlinear fractional stochastic neutral integro-differential equations with Poisson jumps and infinite delay in Hilbert space. Initially, the existence and uniqueness of mild solution for the proposed system are verified by applying the suitable conditions of sectorial operators, fixed point technique and stochastic analysis with non-Lipschitz condition and Lipschitz condition as a special case. Also, continuous dependence of mild solutions for proposed model is determined. Finally an example is provided to illustrate the developed theory.