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The Necessary Conditions of Fractional Optimal Control in the Sense of Caputo

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  • Tian Liang Guo

    (Anhui University)

Abstract

This paper deals with the optimal control problem of a fractional dynamic system in the sense of Caputo. The main result of this paper gives a second order necessary optimality condition for fractional optimal control problems, which has not been discussed before. An application is introduced to explain our main results.

Suggested Citation

  • Tian Liang Guo, 2013. "The Necessary Conditions of Fractional Optimal Control in the Sense of Caputo," Journal of Optimization Theory and Applications, Springer, vol. 156(1), pages 115-126, January.
    • Handle: RePEc:spr:joptap:v:156:y:2013:i:1:d:10.1007_s10957-012-0233-0
    DOI: 10.1007/s10957-012-0233-0
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    Citations

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    Cited by:

    1. Dumitru Baleanu & Amin Jajarmi & Mojtaba Hajipour, 2017. "A New Formulation of the Fractional Optimal Control Problems Involving Mittag–Leffler Nonsingular Kernel," Journal of Optimization Theory and Applications, Springer, vol. 175(3), pages 718-737, December.
    2. Meghadri Das & Guruprasad Samanta & Manuel De la Sen, 2021. "Stability Analysis and Optimal Control of a Fractional Order Synthetic Drugs Transmission Model," Mathematics, MDPI, vol. 9(7), pages 1-34, March.
    3. Tirumalasetty Chiranjeevi & Raj Kumar Biswas, 2017. "Discrete-Time Fractional Optimal Control," Mathematics, MDPI, vol. 5(2), pages 1-12, April.
    4. Heydari, M.H. & Hooshmandasl, M.R. & Maalek Ghaini, F.M. & Cattani, C., 2016. "Wavelets method for solving fractional optimal control problems," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 139-154.
    5. 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.
    6. Surendra Kumar, 2017. "Mild Solution and Fractional Optimal Control of Semilinear System with Fixed Delay," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 108-121, July.
    7. Rafał Kamocki & Marek Majewski, 2017. "On the Existence and Continuous Dependence on Parameter of Solutions to Some Fractional Dirichlet Problem with Application to Lagrange Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 32-46, July.
    8. Chongyang Liu & Zhaohua Gong & Changjun Yu & Song Wang & Kok Lay Teo, 2021. "Optimal Control Computation for Nonlinear Fractional Time-Delay Systems with State Inequality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 83-117, October.
    9. Meghadri Das & Guruprasad Samanta & Manuel De la Sen, 2021. "A Fractional Ordered COVID-19 Model Incorporating Comorbidity and Vaccination," Mathematics, MDPI, vol. 9(21), pages 1-27, November.
    10. Loïc Bourdin & Rui A. C. Ferreira, 2021. "Legendre’s Necessary Condition for Fractional Bolza Functionals with Mixed Initial/Final Constraints," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 672-708, August.

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