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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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    References listed on IDEAS

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    1. Zihan Gao & Tianlin Hu & Huihui Pang, 2020. "Existence and Uniqueness Theorems for a Fractional Differential Equation with Impulsive Effect under Band‐Like Integral Boundary Conditions," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    2. Karim Guida & Lahcen Ibnelazyz & Khalid Hilal & Said Melliani, 2021. "Existence and Uniqueness of Solutions for Coupled Impulsive Fractional Pantograph Differential Equations with Antiperiodic Boundary Conditions," Advances in Mathematical Physics, Hindawi, vol. 2021, pages 1-11, May.
    3. Tianzeng Li & Yu Wang & Weiqiu Pan, 2021. "Parameter Estimation for the One-Term (Multiterm) Fractional-Order SEIAR Models of Norovirus Outbreak," Advances in Mathematical Physics, Hindawi, vol. 2021, pages 1-16, June.
    4. Singh, Harendra, 2020. "Analysis for fractional dynamics of Ebola virus model," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    5. Tianzeng Li & Yu Wang & Weiqiu Pan, 2021. "Parameter Estimation for the One‐Term (Multiterm) Fractional‐Order SEIAR Models of Norovirus Outbreak," Advances in Mathematical Physics, John Wiley & Sons, vol. 2021(1).
    6. Usman Riaz & Akbar Zada & Zeeshan Ali & Manzoor Ahmad & Jiafa Xu & Zhengqing Fu, 2019. "Analysis of Nonlinear Coupled Systems of Impulsive Fractional Differential Equations with Hadamard Derivatives," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-20, June.
    7. Mohamed Hannabou & Hilal Khalid, 2019. "Investigation of a Mild Solution to Coupled Systems of Impulsive Hybrid Fractional Differential Equations," International Journal of Differential Equations, Hindawi, vol. 2019, pages 1-9, December.
    8. Arshad Ali & Vidushi Gupta & Thabet Abdeljawad & Kamal Shah & Fahd Jarad, 2020. "Mathematical Analysis of Nonlocal Implicit Impulsive Problem under Caputo Fractional Boundary Conditions," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-16, November.
    9. Karim Guida & Lahcen Ibnelazyz & Khalid Hilal & Said Melliani, 2021. "Existence and Uniqueness of Solutions for Coupled Impulsive Fractional Pantograph Differential Equations with Antiperiodic Boundary Conditions," Advances in Mathematical Physics, John Wiley & Sons, vol. 2021(1).
    10. Zihan Gao & Tianlin Hu & Huihui Pang, 2020. "Existence and Uniqueness Theorems for a Fractional Differential Equation with Impulsive Effect under Band-Like Integral Boundary Conditions," Advances in Mathematical Physics, Hindawi, vol. 2020, pages 1-8, January.
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