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Relaxed Controls for Nonlinear Fractional Impulsive Evolution Equations

Author

Listed:
  • JinRong Wang

    (Guizhou University)

  • Michal Fec̆kan

    (Comenius University
    Slovak Academy of Sciences)

  • Yong Zhou

    (Xiangtan University)

Abstract

In this paper, we study optimal relaxed controls and relaxation of nonlinear fractional impulsive evolution equations. Firstly, existence of piecewise continuous mild solutions for the original fractional impulsive control system is presented. Secondly, fractional impulsive relaxed control system is constructed by using a regular countably additive measure and making the original control system convexified. Thirdly, optimal relaxed controls and relaxation theorems are obtained. Finally, application to initial-boundary value problem of fractional impulsive parabolic control system is considered.

Suggested Citation

  • JinRong Wang & Michal Fec̆kan & Yong Zhou, 2013. "Relaxed Controls for Nonlinear Fractional Impulsive Evolution Equations," Journal of Optimization Theory and Applications, Springer, vol. 156(1), pages 13-32, January.
    • Handle: RePEc:spr:joptap:v:156:y:2013:i:1:d:10.1007_s10957-012-0170-y
    DOI: 10.1007/s10957-012-0170-y
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    References listed on IDEAS

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    1. JinRong Wang & Yong Zhou & Milan Medveď, 2012. "On the Solvability and Optimal Controls of Fractional Integrodifferential Evolution Systems with Infinite Delay," Journal of Optimization Theory and Applications, Springer, vol. 152(1), pages 31-50, January.
    2. JinRong Wang & Zhenbin Fan & Yong Zhou, 2012. "Nonlocal Controllability of Semilinear Dynamic Systems with Fractional Derivative in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 292-302, July.
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    Cited by:

    1. Shengda Liu & JinRong Wang, 2017. "Optimal Controls of Systems Governed by Semilinear Fractional Differential Equations with Not Instantaneous Impulses," Journal of Optimization Theory and Applications, Springer, vol. 174(2), pages 455-473, August.
    2. Yan, Zuomao & Lu, Fangxia, 2017. "Approximate controllability of a multi-valued fractional impulsive stochastic partial integro-differential equation with infinite delay," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 425-447.
    3. JinRong Wang & Michal Fečkan & Amar Debbouche, 2019. "Time Optimal Control of a System Governed by Non-instantaneous Impulsive Differential Equations," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 573-587, August.
    4. 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.
    5. 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.
    6. shu, Xiao-Bao & Shi, Yajing, 2016. "A study on the mild solution of impulsive fractional evolution equations," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 465-476.

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