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Discontinuity, Nonlinearity, and Complexity 15(3) (2026) 381--394 | DOI:10.5890/DNC.2026.09.007

Wadii Ghandor$^{1}$, Ahmed Aberqi$^{2}$, Zoubida Ech-chaffani$^{1}$, Touria Karite$^{2}$

$^{1}$ Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, Fez 30050, Morocco

$^{2}$ Applied sciences & Emerging Technologies Laboratory (LSATE), National School of Applied Sciences, Sidi Mohamed ben Abdellah University, Avenue My Abdallah Km 5 Route d'Imouzzer, Fez, BP 72, Morocco

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Abstract

This paper investigates the controllability of linear fractional-order control systems featuring both state and control delays, using the Riemann-Liouville fractional derivative framework. An explicit representation of the system's solution is derived, enabling the formulation of a controllability criterion based on the rank condition. We establish necessary and sufficient conditions ensuring controllability of the considered class of fractional systems. To validate the theoretical results, a numerical example is provided and discussed. In particular, a numerical simulation is carried out to illustrate the behavior of the system under the designed control law. The evolution of the state trajectories and the applied control input are plotted, showing the impact of the delay and the fractional-order dynamics on the system performance.

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