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On a Periodic Boundary Value Problem for a Fractional–Order Semilinear Functional Differential Inclusions in a Banach Space

Author

Listed:
  • Mikhail Kamenski

    (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, Taichung 40447, Taiwan)

Abstract

We consider the periodic boundary value problem (PBVP) for a semilinear fractional-order delayed functional differential inclusion in a Banach space. We introduce and study a multivalued integral operator whose fixed points coincide with mild solutions of our problem. On that base, we prove the main existence result (Theorem 4). We present an example dealing with existence of a trajectory for a time-fractional diffusion type feedback control system with a delay satisfying periodic boundary value condition.

Suggested Citation

  • Mikhail Kamenski & Valeri Obukhovskii & Garik Petrosyan & Jen-Chih Yao, 2019. "On a Periodic Boundary Value Problem for a Fractional–Order Semilinear Functional Differential Inclusions in a Banach Space," Mathematics, MDPI, vol. 7(12), pages 1-14, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1146-:d:290225
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