Optimal controls for fractional stochastic differential systems driven by Rosenblatt process with impulses

Abstract

The objective of this article is to consider a new class of fractional stochastic differential systems driven by the Rosenblatt process with impulses. We used fractional calculus, stochastic analysis, and Krasnoselskii's fixed point theorem to study the existence of piecewise continuous mild solutions for the proposed system. Further, we discussed the existence of optimal controls for the considered system. Our main results are well supported by an illustrative example.

Optimal controls of impulsive fractional stochastic differential systems driven by Rosenblatt process with state‐dependent delay

“…The optimal controls play a significant role in the designing of stochastic control systems. Optimal control problem for fractional differential equations has been investigated by several authors; see for instance [33][34][35][36][37] and the references therein. Harrat et al [38] analyzed the existence of optimal controls for impulsive Hilfer fractional evolution inclusion with Clarke subdifferential.…”

Approximate controllability of Atangana- Baleanu fractional stochastic differential systems with non-Gaussian process and impulses

“…The models of this situation are created using non-instantaneous impulses. For more knowledge about non-instantaneous impulses and their applications, see [2,15,18,22,37,38,41] and the references therein. Yan [40] discussed the optimal controls for stochastic evolution inclusions of Clarke subdifferential type with impulses.…”