Reachability of fractional dynamical systems with multiple delays in control using ψ-Hilfer pseudo-fractional derivative

Abstract

In this article, we study the reachability of linear and non-linear fractional dynamical systems with multiple delays in control in the sense of the ψ-Hilfer pseudo-fractional derivative. The necessary and sufficient conditions for the reachability of linear fractional dynamical systems are obtained using the Gramian matrix, which is expressed by Mittag–Leffler functions. Sufficient conditions for the reachability of nonlinear fractional dynamical systems are obtained by using Schauder’s fixed point theorem. Two numerical examples are offered to help better understand the theoretical results.