Existence, averaging principle and trajectory controllability for neutral impulsive fractional stochastic differential evolution system

This work concerns with the study on existence, averaging principle, and trajectory controllability (TC) on neutral impulsive fractional stochastic differential evolution equations (NIFSDEs) with infinite time delay driven by Poisson jumps and fractional Brownian motion (fBm). Initially, by considering sufficient Carathéodory conditions, and using Carathéodory approximation technique, fractional calculus and stochastic analysis, the existence results are obtained. Then, the averaging principle for the class of observed system is investigated in mean square sense. In the later part, the TC for the proposed system is studied. To support the acquired theoretical results, an application is furnished.