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On the Fractional Optimal Control Problems with Singular and Non–Singular Derivative Operators: A Mathematical Derive

Author

Listed:
  • Tim Chen

    (Department of Mathematics, Cankaya University, 06530 Ankara, Turkey Department of Electrical Engineering, University of Bojnord, Bojnord, Iran)

  • Bunnitru Daleanu

    (Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia Institute of Space Sciences, Magurele–Bucharest, Romania)

  • J. C.-Y. Chen*

    (NAAM Research Group, King Abdulaziz University, Jeddah 21589, Saudi Arabia St Petersburg Univ, Dept Math & Mech, Univ Skii 28, St Petersburg 198504, Russia)

Abstract

The aim of this paper is to design an efficient numerical method to solve a class of time fractional optimal control problems. In this problem formulation, the fractional derivative operator is consid- ered in three cases with both singular and non–singular kernels. The necessary conditions are derived for the optimality of these problems and the proposed method is evaluated for different choices of derivative operators. Simulation results indicate that the suggested technique works well and pro- vides satisfactory results with considerably less computational time than the other existing methods. Comparative results also verify that the fractional operator with Mittag–Leffler kernel in the Caputo sense improves the performance of the controlled system in terms of the transient response compared to the other fractional and integer derivative operators.

Suggested Citation

  • Tim Chen & Bunnitru Daleanu & J. C.-Y. Chen*, 2018. "On the Fractional Optimal Control Problems with Singular and Non–Singular Derivative Operators: A Mathematical Derive," Scientific Review, Academic Research Publishing Group, vol. 4(12), pages 95-98, 12-2018.
    • Handle: RePEc:arp:srarsr:2018:p:95-98
    DOI: 10.32861/sr.412.95.98
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    References listed on IDEAS

    as
    1. Ali Lotfi, 2017. "A Combination of Variational and Penalty Methods for Solving a Class of Fractional Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 65-82, July.
    2. Jajarmi, Amin & Hajipour, Mojtaba & Baleanu, Dumitru, 2017. "New aspects of the adaptive synchronization and hyperchaos suppression of a financial model," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 285-296.
    3. Jajarmi, Amin & Baleanu, Dumitru, 2018. "A new fractional analysis on the interaction of HIV with CD4+ T-cells," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 221-229.
    4. Nastaran Ejlali & Seyed Mohammad Hosseini, 2017. "A Pseudospectral Method for Fractional Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 83-107, July.
    5. Salman Jahanshahi & Delfim F. M. Torres, 2017. "A Simple Accurate Method for Solving Fractional Variational and Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 156-175, July.
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