Boundary controllability of Caputo fractional differential equations

Abstract

The goal of the paper is to study the existence of mild solutions and the exact controllability of an abstract Caputo-fractional system with semilinear boundary control in Banach spaces. Sufficient criteria for the existence of mild solutions and controllability for the desired issue are provided, based on Schauder's fixed point theorem. Moreover, for fractional linear boundary control, we present a characterization of controllability using a standard fractional linear system with internal control. We provide an example to demonstrate the viability of our theoretical findings.