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Existence and Optimal Controls for Fractional Stochastic Evolution Equations of Sobolev Type Via Fractional Resolvent Operators

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  • Yong-Kui Chang

    (Xidian University)

  • Yatian Pei

    (Xidian University)

  • Rodrigo Ponce

    (Universidad de Talca)

Abstract

This paper is mainly concerned with controlled stochastic evolution equations of Sobolev type for the Caputo and Riemann–Liouville fractional derivatives. Some sufficient conditions are established for the existence of mild solutions and optimal state-control pairs of the limited Lagrange optimal systems. The main results are investigated by compactness of fractional resolvent operator family, and the optimal control results are derived without uniqueness of solutions for controlled evolution equations.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:182:y:2019:i:2:d:10.1007_s10957-018-1314-5
    DOI: 10.1007/s10957-018-1314-5
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    References listed on IDEAS

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    1. 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.
    2. Rodrigo Ponce, 2016. "Existence of Mild Solutions to Nonlocal Fractional Cauchy Problems via Compactness," Abstract and Applied Analysis, Hindawi, vol. 2016, pages 1-15, September.
    3. 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.
    4. Revathi, P. & Sakthivel, R. & Ren, Yong, 2016. "Stochastic functional differential equations of Sobolev-type with infinite delay," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 68-77.
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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. Yao-Qun Wu & Jia Wei He, 2022. "Existence and Optimal Controls for Hilfer Fractional Sobolev-Type Stochastic Evolution Equations," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 79-101, October.
    3. Wang, Guotao & Qin, Jianfang & Zhang, Lihong & Baleanu, Dumitru, 2020. "Explicit iteration to a nonlinear fractional Langevin equation with non-separated integro-differential strip-multi-point boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).

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