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Existence and Optimal Controls for Hilfer Fractional Sobolev-Type Stochastic Evolution Equations

Author

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  • Yao-Qun Wu

    (Shaoyang University)

  • Jia Wei He

    (Guangxi University)

Abstract

This paper investigates the Sobolev-type problems for Hilfer fractional stochastic evolution equations and optimal controls in Hilbert spaces. With the help of a characteristic solution operator and its properties, we present an existence of mild solutions to the fractional stochastic evolution equations. Moreover, some sufficient conditions are established for the existence conditions of optimal state control pairs of the limited Lagrange optimal systems. Our methods are based on the fractional calculus, Hölder inequality, stochastic analysis and fixed point theorem.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:195:y:2022:i:1:d:10.1007_s10957-022-02059-2
    DOI: 10.1007/s10957-022-02059-2
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    References listed on IDEAS

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    6. 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.
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