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Existence and optimal controls of non-autonomous impulsive integro-differential evolution equation with nonlocal conditions

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  • Yang, He
  • Zhao, Yanxia

Abstract

In this paper, the existence of solutions and optimal state-control pair of non-autonomous impulsive integro-differential evolution equation with nonlocal conditions in abstract spaces are investigated. By using the Krasnoselskii’s fixed point theorem, we first prove the existence of mild solutions of the concerned problem. Then without the Lipschitz continuity of the nonlinearity, the existence of optimal state-control pair of control system governed by impulsive integro-differential evolution equations is presented by constructing minimizing sequences twice. An example is given as an application of the abstract results.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:148:y:2021:i:c:s0960077921003817
    DOI: 10.1016/j.chaos.2021.111027
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Yong-Kui Chang & Yatian Pei & Rodrigo Ponce, 2019. "Existence and Optimal Controls for Fractional Stochastic Evolution Equations of Sobolev Type Via Fractional Resolvent Operators," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 558-572, August.
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    Cited by:

    1. Fan Zhang & Heng-You Lan & Hai-Yang Xu, 2022. "Generalized Hukuhara Weak Solutions for a Class of Coupled Systems of Fuzzy Fractional Order Partial Differential Equations without Lipschitz Conditions," Mathematics, MDPI, vol. 10(21), pages 1-21, October.

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