Approximate Controllability for Hilfer Fractional Stochastic Non-instantaneous Impulsive Differential System with Rosenblatt Process and Poisson Jumps

Abstract

This paper discusses the approximate controllability of Hilfer fractional stochastic differential system involving non-instantaneous impulses with Rosenblatt process and Poisson jumps. By utilising stochastic analysis, semigroup theory, fractional calculus, and Krasnoselskii’s fixed point theorem, we prove our primary outcomes. Firstly, we prove the approximate controllability of the Hilfer fractional system. As a final step, we provide an example to highlight our discussion.