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On the Existence of a Unique Solution for a Class of Fractional Differential Inclusions in a Hilbert Space

Author

Listed:
  • Mikhail Kamenskii

    (Faculty of Mathematics, Voronezh State University, Voronezh 394018, Russia)

  • Valeri Obukhovskii

    (Faculty of Physics and Mathematics, Voronezh State Pedagogical University, Voronezh 394043, Russia)

  • Garik Petrosyan

    (Research Center of Voronezh State University of Engineering Technologies and Faculty of Physics and Mathematics, Voronezh State Pedagogical University, Voronezh 394043, Russia)

  • Jen-Chih Yao

    (Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan)

Abstract

We obtained results on the existence and uniqueness of a mild solution for a fractional-order semi-linear differential inclusion in a Hilbert space whose right-hand side contains an unbounded linear monotone operator and a Carathéodory-type multivalued nonlinearity satisfying some monotonicity condition in the phase variables. We used the Yosida approximations of the linear part of the inclusion, the method of a priori estimates of solutions, and the topological degree method for condensing vector fields. As an example, we considered the existence and uniqueness of a solution to the Cauchy problem for a system governed by a perturbed subdifferential inclusion of a fractional diffusion type.

Suggested Citation

  • Mikhail Kamenskii & Valeri Obukhovskii & Garik Petrosyan & Jen-Chih Yao, 2021. "On the Existence of a Unique Solution for a Class of Fractional Differential Inclusions in a Hilbert Space," Mathematics, MDPI, vol. 9(2), pages 1-19, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:2:p:136-:d:477972
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    Cited by:

    1. Jimin Yu & Zeming Zhao & Yabin Shao, 2023. "On Cauchy Problems of Caputo Fractional Differential Inclusion with an Application to Fractional Non-Smooth Systems," Mathematics, MDPI, vol. 11(3), pages 1-18, January.

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