Examining reachability of fractional dynamical systems with delays in control utilizing ψ-Hilfer pseudo-fractional derivative

Abstract

This research focuses on the reachability criteria of fractional dynamical systems with delays in control of order ϑ ∈ (0, 1) and type ϱ ∈ [0, 1] in the context of control theory. The study introduces the utilization of the ψ-Hilfer pseudo fractional derivative to describe the dynamics of systems with delays in control. We obtained the necessary and sufficient conditions for the reachability criteria of fractional order linear dynamical systems by employing the positive definiteness of Gramian matrices. We arrived the sufficient conditions for the reachability criteria of fractional order nonlinear dynamical systems using Banach’s fixed point theorem. A few numerical examples are made available for a better understanding of the theoretical conclusions.