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

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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.

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Acknowledgements

The authors are grateful to the editor and anonymous referees for carefully reading this manuscript and giving valuable suggestion for improvements. The first author was partially supported by NSFRP of Shaanxi Province (2017JM1017). The third author was partially supported by Fondecyt 11130619.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xidian University, Xi’an, 710071, Shaanxi, People’s Republic of China

    Yong-Kui Chang & Yatian Pei

  2. Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile

    Rodrigo Ponce

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  1. Yong-Kui Chang
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  2. Yatian Pei
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  3. Rodrigo Ponce
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Correspondence to Yong-Kui Chang.

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Chang, YK., Pei, Y. & Ponce, R. Existence and Optimal Controls for Fractional Stochastic Evolution Equations of Sobolev Type Via Fractional Resolvent Operators. J Optim Theory Appl 182, 558–572 (2019). https://doi.org/10.1007/s10957-018-1314-5

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  • DOI: https://doi.org/10.1007/s10957-018-1314-5

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