Approximate Controllability of Impulsive Non-local Non-linear Fractional Dynamical Systems and Optimal Control

TL;DR

This paper investigates the approximate controllability and optimal control of impulsive non-local non-linear fractional dynamical systems in Banach spaces, using advanced mathematical tools like fractional calculus and fixed point theorems.

Contribution

It introduces new existence and controllability results for a broad class of fractional systems with impulses and non-local conditions, along with optimal control solutions.

Findings

Established approximate controllability under non-linear conditions.

Proved existence of optimal control pairs with a Bolza cost functional.

Utilized fractional calculus and fixed point theorems for main results.

Abstract

We establish existence, approximate controllability and optimal control of a class of impulsive non-local non-linear fractional dynamical systems in Banach spaces. We use fractional calculus, sectorial operators and Krasnoselskii fixed point theorems for the main results. Approximate controllability results are discussed with respect to the inhomogeneous non-linear part. Moreover, we prove existence results of optimal pairs of corresponding fractional control systems with a Bolza cost functional.