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Investigation of controllability and stability of fractional dynamical systems with delay in control

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  • Selvam, Anjapuli Panneer
  • Govindaraj, Venkatesan

Abstract

The primary objective of this research is to investigate the controllability and Hyers–Ulam stability of fractional dynamical systems represented by ψ-Caputo fractional derivative with delay in control. To establish the necessary and sufficient conditions for assessing the controllability of linear fractional systems, which are notably distinguished by the presence of Mittag-Leffler functions, we employ the positivity of the Grammian matrix. Also, we present sufficient conditions for the controllability requirements for nonlinear fractional systems utilizing the fixed-point technique. The Hyers-Ulam stability technique is used to determine the sufficient condition for the stability of fractional nonlinear systems with delay in control. Numerical instances are provided to enhance comprehension of the theoretical findings.

Suggested Citation

  • Selvam, Anjapuli Panneer & Govindaraj, Venkatesan, 2024. "Investigation of controllability and stability of fractional dynamical systems with delay in control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 89-104.
    • Handle: RePEc:eee:matcom:v:220:y:2024:i:c:p:89-104
    DOI: 10.1016/j.matcom.2024.01.011
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    References listed on IDEAS

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    1. Nazim I. Mahmudov & Yansheng Liu, 2022. "Analytical Solution of the Fractional Linear Time-Delay Systems and their Ulam-Hyers Stability," Journal of Applied Mathematics, Hindawi, vol. 2022, pages 1-7, September.
    2. Muath Awadalla & Yves Yannick Yameni Noupoue & Kinda Abu Asbeh & Noureddine Ghiloufi & Arzu Akbulut, 2022. "Modeling Drug Concentration Level in Blood Using Fractional Differential Equation Based on Psi-Caputo Derivative," Journal of Mathematics, Hindawi, vol. 2022, pages 1-8, September.
    3. Liu, Kui & Wang, JinRong & Zhou, Yong & O’Regan, Donal, 2020. "Hyers–Ulam stability and existence of solutions for fractional differential equations with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    4. Ahmed M. Elshenhab & Xingtao Wang & Omar Bazighifan & Jan Awrejcewicz, 2022. "Finite-Time Stability Analysis of Linear Differential Systems with Pure Delay," Mathematics, MDPI, vol. 10(9), pages 1-10, April.
    5. Shah, Kamal & Abdeljawad, Thabet & Ali, Arshad, 2022. "Mathematical analysis of the Cauchy type dynamical system under piecewise equations with Caputo fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    6. Khan, Hasib & Ibrahim, Muhammad & Abdel-Aty, Abdel-Haleem & Khashan, M. Motawi & Khan, Farhat Ali & Khan, Aziz, 2021. "A fractional order Covid-19 epidemic model with Mittag-Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
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