Controllability and optimal control for fractional neutral evolution systems with Caputo derivative

Abstract

The purpose of this paper is to study the controllability of a class of fractional neutral evolution equations involving Caputo fractional derivative of order $\alpha\in ]0,1[$. First, we prove the result with the help of fractional calculus theory, semi-group theory and Banach fixed point theorem under some assumptions, then we concentrate on the determination of a control achieving this kind of controllability with minimum energy. An example is given to validate the obtained results.