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

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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.

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Acknowledgements

The authors would like to thank all the anonymous reviewers and the editors for their helpful advices.

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Authors and Affiliations

  1. School of Information Engineering, Shaoyang University, Hunan, 422000, China

    Yao-Qun Wu

  2. College of Mathematics and Information Science, Guangxi University, Nanning, 530004, China

    Jia Wei He

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  1. Yao-Qun Wu
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  2. Jia Wei He
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Correspondence to Jia Wei He.

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Communicated by Aram Arutyunov.

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Wu, YQ., He, J.W. Existence and Optimal Controls for Hilfer Fractional Sobolev-Type Stochastic Evolution Equations. J Optim Theory Appl 195, 79–101 (2022). https://doi.org/10.1007/s10957-022-02059-2

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