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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Reachability of Fractional Dynamical Systems with Distributed Delays in Control using $psi$-Hilfer Pseudo-Fractional Derivative

Discontinuity, Nonlinearity, and Complexity 13(4) (2024) 609--620 | DOI:10.5890/DNC.2024.12.003

A. Panneer Selvam, V. Govindaraj

Department of Mathematics, National Institute of Technology Puducherry, Karaikal - 609 609, India

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Abstract

This research investigates the reachability of linear and non-linear fractional dynamical systems with distributed delays in control using the $\psi$-Hilfer pseudo-fractional derivative in g-calculus. Grammian matrices, which are characterized by Mittag-Leffler functions, are used to provide necessary and sufficient criteria for reachability in the linear case, while Schauder's fixed point theorem is used to create sufficient conditions for reachability in the nonlinear case. A couple of numerical results is offered to explain the theoretical results.

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