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On the Solvability and Optimal Controls of Fractional Integrodifferential Evolution Systems with Infinite Delay

Author

Listed:
  • JinRong Wang

    (Guizhou University)

  • Yong Zhou

    (Xiangtan University)

  • Milan Medveď

    (Comenius University)

Abstract

In this paper, we study the solvability and optimal controls of a class of fractional integrodifferential evolution systems with infinite delay in Banach spaces. Firstly, a more appropriate concept for mild solutions is introduced. Secondly, existence and continuous dependence of mild solutions are investigated by utilizing the techniques of a priori estimation and extension of step by steps. Finally, existence of optimal controls for system governed by fractional integrodifferential evolution systems with infinite delay is proved.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:152:y:2012:i:1:d:10.1007_s10957-011-9892-5
    DOI: 10.1007/s10957-011-9892-5
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    Citations

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    Cited by:

    1. Michal Fec̆kan & JinRong Wang & Yong Zhou, 2013. "Controllability of Fractional Functional Evolution Equations of Sobolev Type via Characteristic Solution Operators," Journal of Optimization Theory and Applications, Springer, vol. 156(1), pages 79-95, January.
    2. Shouguo Zhu & Zhenbin Fan & Gang Li, 2017. "Optimal Controls for Riemann–Liouville Fractional Evolution Systems without Lipschitz Assumption," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 47-64, July.
    3. 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.
    4. Wang, JinRong, 2015. "Approximate mild solutions of fractional stochastic evolution equations in Hilbert spaces," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 315-323.
    5. Peng, Li & Zhou, Yong & Debbouche, Amar, 2019. "Approximation techniques of optimal control problems for fractional dynamic systems in separable Hilbert spaces," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 234-241.
    6. 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.
    7. Čermák, Jan & Došlá, Zuzana & Kisela, Tomáš, 2017. "Fractional differential equations with a constant delay: Stability and asymptotics of solutions," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 336-350.
    8. 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.
    9. P. Balasubramaniam & P. Tamilalagan, 2017. "The Solvability and Optimal Controls for Impulsive Fractional Stochastic Integro-Differential Equations via Resolvent Operators," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 139-155, July.
    10. Surendra Kumar & Shobha Yadav, 2021. "Infinite-delayed stochastic impulsive differential systems with Poisson jumps," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(2), pages 344-362, June.

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