Examining reachability criteria for fractional dynamical systems with mixed delays in control utilizing ψ-Hilfer pseudo-fractional derivative

Anjapuli Panneer Selvam, Venkatesan Govindaraj and Hijaz Ahmad

Chaos, Solitons & Fractals, 2024, vol. 181, issue C

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.

Keywords: Fractional calculus; ψ-Hilfer pseudo-fractional derivative; Delay dynamical systems; Reachability Grammian; Fixed point theorem (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:181:y:2024:i:c:s0960077924002546

DOI: 10.1016/j.chaos.2024.114702

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