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

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

Mathematics, 2021, vol. 9, issue 2, 1-19

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.

Keywords: fractional differential inclusion; semi-linear differential inclusion; Cauchy problem; monotonicity condition; existence; uniqueness; a priori estimate; Yosida approximation; condensing operator; topological degree (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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