Examining reachability criteria for fractional dynamical systems with mixed delays in control utilizing [formula omitted]-Hilfer pseudo-fractional derivative

Abstract

The main objective of the present article is to employ the ψ-Hilfer pseudo-fractional derivative (HPFD) to examine the reachability criteria for fractional dynamical systems with mixed delays in control of order ϑ∈(0,1) and type ϱ∈[0,1]. we derived the sufficient and necessary conditions for the reachability criterion of fractional linear dynamical systems by utilizing the positiveness of Grammian matrices, which are defined by the Mittag-Leffler functions. The sufficient conditions for the reachability criteria of fractional nonlinear dynamical systems are obtained by using Banach’s fixed point theorem. To help grasp the theoretical results, only a limited number of numerical examples are provided.