Exact controllability of conformable linear systems with semilinear boundary control

Abstract

In this manuscript, we investigate the exact controllability of a class of linear systems governed by conformable fractional derivatives of order α in (0; 1] subject to semilinear boundary control in Banach spaces. We first establish the existence of mild solutions to the associated fractional Cauchy problems. We then derive sufficient conditions ensuring the exact controllability of these conformable linear systems under semilinear boundary control actions. An abstract model of an age-structured population dynamics system is provided to illustrate the applicability of the theoretical results.