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Optimal Feedback Control Results for Hilfer Fractional Neutral Dynamical Systems with History-Dependent Operators

Author

Listed:
  • Shanmugam Vivek

    (Vellore Institute of Technology)

  • Sumati Kumari Panda

    (GMR Institute of Technology)

  • Velusamy Vijayakumar

    (Vellore Institute of Technology)

Abstract

This paper presents a systematic approach for analyzing optimal feedback control systems governed by Hilfer fractional neutral evolution equations with history-dependent operators in separable reflexive Banach spaces. We initially investigate the existence of mild solutions for the system using the Darbo-Sadovskii fixed point theorem. Subsequently, feasible pairs were established by applying the Filippov theorem and the Cesari property. Furthermore, we demonstrate the existence of optimal control pairs for the associated Lagrange control problem. Finally, an illustration is provided to highlight the effectiveness of our findings.

Suggested Citation

  • Shanmugam Vivek & Sumati Kumari Panda & Velusamy Vijayakumar, 2025. "Optimal Feedback Control Results for Hilfer Fractional Neutral Dynamical Systems with History-Dependent Operators," Journal of Optimization Theory and Applications, Springer, vol. 204(2), pages 1-23, February.
    • Handle: RePEc:spr:joptap:v:204:y:2025:i:2:d:10.1007_s10957-024-02586-0
    DOI: 10.1007/s10957-024-02586-0
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    References listed on IDEAS

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    1. P. Balasubramaniam & P. Tamilalagan, 2017. "The Solvability and Optimal Controls for Impulsive Fractional Stochastic Integro-Differential Equations via Resolvent Operators," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 139-155, July.
    2. Gu, Haibo & Trujillo, Juan J., 2015. "Existence of mild solution for evolution equation with Hilfer fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 344-354.
    3. Debbouche, Amar & Antonov, Valery, 2017. "Approximate controllability of semilinear Hilfer fractional differential inclusions with impulsive control inclusion conditions in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 140-148.
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