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

Mikhail Kamenski, Valeri Obukhovskii, Garik Petrosyan and Jen-Chih Yao
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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

Mathematics, 2019, vol. 7, issue 12, 1-14

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.

Keywords: fractional functional differential inclusion; semilinear functional differential inclusion; periodic boundary value problem; time-fractional diffusion type feedback control system; fixed point; condensing map; measure of noncompactness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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