On a Periodic Boundary Value Problem for a Fractional–Order Semilinear Functional Differential Inclusions in a Banach Space
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Faculty of Mathematics, Voronezh State University, Voronezh 394018, Russia
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Faculty of Physics and Mathematics, Voronezh State Pedagogical University, Voronezh 394043, Russia
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Research Center of Voronezh State University of Engineering Technologies and Faculty of Physics and Mathematics, Voronezh State Pedagogical University, Voronezh 394043, Russia
4
Research Center for Interneural Computing, China Medical University, Taichung 40447, Taiwan
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Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1146; https://doi.org/10.3390/math7121146
Received: 28 October 2019 / Revised: 16 November 2019 / Accepted: 18 November 2019 / Published: 23 November 2019
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications)
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.
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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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
MDPI and ACS Style
Kamenski, M.; Obukhovskii, V.; Petrosyan, G.; Yao, J.-C. On a Periodic Boundary Value Problem for a Fractional–Order Semilinear Functional Differential Inclusions in a Banach Space. Mathematics 2019, 7, 1146.
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