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An Analysis of Controllability Criteria for Higher‐Order Caputo Fractional Differential Systems With State and Control Delays

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Listed:
  • Anjapuli Panneer Selvam
  • Venkatesan Govindaraj
  • Raaid Alubady
  • Sina Etemad

Abstract

The present study investigates the controllability problems for higher‐order semilinear fractional differential systems (HOSLFDSs) with state and control delays in the context of the Caputo fractional derivative. Exploiting the invertibility of the Gramian matrix of fractional order, the necessary and sufficient conditions for the controllability results associated with higher‐order linear fractional differential systems (HOLFDSs) with state and control delays are determined. Indeed, the Banach fixed‐point theorem and contraction map technique are utilized to derive sufficient conditions for the controllability results associated with HOSLFDSs with state delay, including multiple and distributed delays in control. For a better understanding of the theoretical concepts, this paper also provides several examples with graphical representations.

Suggested Citation

  • Anjapuli Panneer Selvam & Venkatesan Govindaraj & Raaid Alubady & Sina Etemad, 2025. "An Analysis of Controllability Criteria for Higher‐Order Caputo Fractional Differential Systems With State and Control Delays," International Journal of Differential Equations, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jnijde:v:2025:y:2025:i:1:n:5540872
    DOI: 10.1155/ijde/5540872
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    References listed on IDEAS

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    1. Li, Mengmeng & Wang, JinRong, 2018. "Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 254-265.
    2. Vadivoo, B.S. & Jothilakshmi, G. & Almalki, Y. & Debbouche, A. & Lavanya, M., 2022. "Relative controllability analysis of fractional order differential equations with multiple time delays," Applied Mathematics and Computation, Elsevier, vol. 428(C).
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