Minimum Energy Problem in the Sense of Caputo for Fractional Neutral Evolution Systems in Banach Spaces

TL;DR

This paper studies controllability and minimum energy control problems for fractional neutral evolution systems in Banach spaces using Caputo derivatives, providing conditions for solutions and controllability.

Contribution

It introduces new controllability and optimal control conditions for fractional neutral evolution systems in Banach spaces involving Caputo derivatives.

Findings

Established conditions for controllability of fractional neutral systems.

Proved existence of minimum energy solutions using fixed-point and semigroup theories.

Provided a framework for optimal control in fractional evolution equations.

Abstract

We investigate a class of fractional neutral evolution equations on Banach spaces involving Caputo derivatives. Main results establish conditions for the controllability of the fractional-order system and conditions for existence of a solution to an optimal control problem of minimum energy. The results are proved with the help of fixed-point and semigroup theories.