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

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  • Selvam, Anjapuli Panneer
  • Govindaraj, Venkatesan
  • Ahmad, Hijaz

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.

Suggested Citation

  • Selvam, Anjapuli Panneer & Govindaraj, Venkatesan & Ahmad, Hijaz, 2024. "Examining reachability criteria for fractional dynamical systems with mixed delays in control utilizing ψ-Hilfer pseudo-fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:chsofr:v:181:y:2024:i:c:s0960077924002546
    DOI: 10.1016/j.chaos.2024.114702
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    References listed on IDEAS

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    1. Vijayakumar, V. & Udhayakumar, R., 2020. "Results on approximate controllability for non-densely defined Hilfer fractional differential system with infinite delay," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
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