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

Anjapuli Panneer Selvam, Venkatesan Govindaraj, Raaid Alubady and Sina Etemad

International Journal of Differential Equations, 2025, vol. 2025, 1-18

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.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:5540872

DOI: 10.1155/ijde/5540872

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