Dynamical behaviors of fractional neutral stochastic integro-differential delay systems with impulses - Dhanalakshmi Kasinathan; Ramkumar Kasinathan; Ravikumar Kasinathan; Dimplekumar Chalishajar; Dumitru Baleanu (Boundary Value Problems)
Abstract The aim of this manuscript is to analyze the stability for fractional neutral stochastic integro-differential delay systems (FNSIDDSs) with impulses driven by Poisson jumps. Sufficient conditions are established for a class of FNSIDDSs with impulses driven by Poisson jumps with the help of fractional calculus, stochastic theory, semigroup theory, and Mönch fixed point theorem in an infinite-dimensional space followed by the existence of a mild solution. The main reason for using Mönch fixed point theorem is its relation to Hausdorff measure of noncompactness (HMNC) adopted to prove the relative compactness conditions. Finally, an example is demonstrated to illustrate the obtained theoretical results.