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Optimal Controls for Riemann–Liouville Fractional Evolution Systems without Lipschitz Assumption

Author

Listed:
  • Shouguo Zhu

    (Yangzhou University
    Taizhou College of Nanjing Normal University)

  • Zhenbin Fan

    (Yangzhou University)

  • Gang Li

    (Yangzhou University)

Abstract

In this paper, an evolution system with a Riemann–Liouville fractional derivative is proposed and analyzed. With the help of a resolvent technique, a suitable concept of solutions to this system is formulated and the corresponding existence of solutions is demonstrated. Furthermore, without the Lipschitz continuity of the nonlinear term, the optimal control result is derived by setting up minimizing sequences twice. Our work essentially generalizes previous results on optimal controls of all evolution systems. Finally, a simple example is presented to illustrate our theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:174:y:2017:i:1:d:10.1007_s10957-017-1119-y
    DOI: 10.1007/s10957-017-1119-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. Fan, Zhenbin, 2014. "Characterization of compactness for resolvents and its applications," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 60-67.
    3. Yang, Min & Wang, Qiru, 2016. "Approximate controllability of Riemann–Liouville fractional differential inclusions," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 267-281.
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    Cited by:

    1. Yang, He & Zhao, Yanxia, 2021. "Existence and optimal controls of non-autonomous impulsive integro-differential evolution equation with nonlocal conditions," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    2. Haq, Abdul, 2022. "Partial-approximate controllability of semi-linear systems involving two Riemann-Liouville fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    3. Liu, Li & Fan, Zhenbin & Li, Gang & Piskarev, Sergey, 2021. "Discrete almost maximal regularity and stability for fractional differential equations in Lp([0, 1], Ω)," Applied Mathematics and Computation, Elsevier, vol. 389(C).
    4. Haq, Abdul & Sukavanam, N., 2022. "Existence and partial approximate controllability of nonlinear Riemann–Liouville fractional systems of higher order," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).

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