Approximate Controllability of Delayed Fractional Stochastic Differential Systems with Mixed Noise and Impulsive Effects

TL;DR

This paper studies the approximate controllability of a new class of impulsive fractional stochastic differential systems with infinite delay driven by mixed fractional Brownian motions, using fixed point methods and fractional calculus.

Contribution

It introduces a novel class of delayed fractional stochastic systems with impulsive effects and establishes their approximate controllability using advanced mathematical techniques.

Findings

Existence of piecewise continuous mild solutions

Conditions for approximate controllability are derived

An illustrative example demonstrates the main results

Abstract

We herein report a new class of impulsive fractional stochastic differential systems driven by mixed fractional Brownian motions with infinite delay and Hurst parameter $\hat{\cal H} \in ( 1/2, 1)$. Using fixed point techniques, a $q$-resolvent family, and fractional calculus, we discuss the existence of a piecewise continuous mild solution for the proposed system. Moreover, under appropriate conditions, we investigate the approximate controllability of the considered system. Finally, the main results are demonstrated with an illustrative example.