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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

Controllability of Proportional Fractional Dynamical Systems

Discontinuity, Nonlinearity, and Complexity 14(2) (2025) 325--336 | DOI:10.5890/DNC.2025.06.007

K. S. Vishnukumar$^1$, M. Matar$^2$, V. Govindaraj$^1$, K. Balachandran$^3$

$^1$ Department of Mathematics, National Institute of Technology Puducherry, Karaikal-609609, India

$^2$ Department of Mathematics, Al-Azhar University-Gaza, Gaza, Palestine

$^3$ Department of Mathematics, Bharathiar University, Coimbatore - 641 046, India

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Abstract

In this study, we explore the controllability of dynamical systems by applying proportional fractional derivatives. The Grammian matrix technique is employed to establish both necessary and sufficient conditions that govern the controllability of linear fractional dynamical systems. Additionally, utilizing Schauder's fixed point theorem, we identify sufficient conditions for the controllability of nonlinear fractional dynamical systems. Numerous examples are provided to demonstrate and elucidate the theoretical findings.

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