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Fractional Order of Evolution Inclusion Coupled with a Time and State Dependent Maximal Monotone Operator

Author

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  • Charles Castaing

    (Département de Mathématiques, Université Montpellier II, Case Courrier 051, 34095 Montpellier CEDEX 5, France)

  • Christiane Godet-Thobie

    (Laboratoire de Mathématiques de Bretagne Atlantique, Université de Bretagne Occidentale, CNRS UMR 6205, 6, Avenue Victor Le Gorgeu, CS 9387, F-29238 Brest CEDEX 3, France)

  • Le Xuan Truong

    (Department of Mathematics and Statistics, University of Economics Ho Chi Minh City, Ho Chi Minh City 700000, Vietnam)

Abstract

This paper is devoted to the study of evolution problems involving fractional flow and time and state dependent maximal monotone operator which is absolutely continuous in variation with respect to the Vladimirov’s pseudo distance. In a first part, we solve a second order problem and give an application to sweeping process. In a second part, we study a class of fractional order problem driven by a time and state dependent maximal monotone operator with a Lipschitz perturbation in a separable Hilbert space. In the last part, we establish a Filippov theorem and a relaxation variant for fractional differential inclusion in a separable Banach space. In every part, some variants and applications are presented.

Suggested Citation

  • Charles Castaing & Christiane Godet-Thobie & Le Xuan Truong, 2020. "Fractional Order of Evolution Inclusion Coupled with a Time and State Dependent Maximal Monotone Operator," Mathematics, MDPI, vol. 8(9), pages 1-30, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1395-:d:401701
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    References listed on IDEAS

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    1. Hiai, Fumio & Umegaki, Hisaharu, 1977. "Integrals, conditional expectations, and martingales of multivalued functions," Journal of Multivariate Analysis, Elsevier, vol. 7(1), pages 149-182, March.
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