Existence and Exponential Stability for Neutral Impulsive Stochastic Integrodifferential Equations with Fractional Brownian Motion Driven by Poisson Jumps

Abstract

In this paper, we establish the results on existence and uniqueness of mild solution of neutral impulsive stochastic integrodifferential equations with fractional Brownian motion driven by Poisson jumps in a Hilbert space. Further, by using an impulsive integral inequality, we study the new sufficient conditions that ensure the exponential stability of mild solution in the mean square moment by utilizing the fractional power of operators and the semigroup theory.