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On the Optimal Control Existence for Multi-Term Multi-Order Fractional Differential Equations with Impulsive Conditions

Author

Listed:
  • HuiChol Choe

    (Kim Il Sung University)

  • SuRim Han

    (Kim Il Sung University)

  • SunAe Pak

    (Kim Il Sung University)

  • GwangHyok Kim

    (Kim Il Sung University)

  • GyongGuk Kim

    (Kim Il Sung University)

  • DanOh U

    (Kim Il Sung University)

Abstract

In this paper, we study the existence of solutions to nonlinear impulsive fractional optimal control problems, where the state equations are linear with respect to their control variables and governed by multi-order systems of multi-term fractional differential ones. Initial and impulsive conditions are also given. The performance index is considered as an integral functional, whose integrand is continuous with respect to its variables. At first, we transform the state equations into the integral ones to prove the existence and uniqueness of solutions, assuming that the nonlinear functions in the equations are Lipschitz continuous in a bounded domain. Secondly, using the generalized Arzela-Ascoli theorem, we establish that sets of our admissible processes are compact ones in a piecewise continuous function space to show the optimal control existence.

Suggested Citation

  • HuiChol Choe & SuRim Han & SunAe Pak & GwangHyok Kim & GyongGuk Kim & DanOh U, 2026. "On the Optimal Control Existence for Multi-Term Multi-Order Fractional Differential Equations with Impulsive Conditions," Journal of Optimization Theory and Applications, Springer, vol. 208(1), pages 1-24, January.
    • Handle: RePEc:spr:joptap:v:208:y:2026:i:1:d:10.1007_s10957-025-02830-1
    DOI: 10.1007/s10957-025-02830-1
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