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 Russian Universities Reports. Mathematics, 2021, Volume 26, Issue 135, Pages 250–270 (Mi vtamu230)

Scientific articles

On the existence of a solution for a periodic boundary value problem for semilinear fractional-order differential inclusions in Banach spaces

M. I. Kamenskiia, V. V. Obukhovskiib, G. Petrosyanb

a Voronezh State University
b Voronezh State Pedagogical University

Abstract: In this paper, we study a periodic boundary value problem for a class of semilinear differential inclusions of fractional order in a Banach space for which the multivalued nonlinearity satisfies the regularity condition expressed in terms of measures of noncompactness. To prove the existence of solutions to the problem, we first construct the corresponding Green function. Then we introduce into consideration a multivalued resolving operator in the space of continuous functions and reduce the posed problem to the existence of fixed points of the resolving multioperator. To prove the existence of a fixed point, a generalized theorem of B.N. Sadovskii type for a condensing multivalued map is used.

Keywords: differential inclusion, fractional derivative, Green's function, condensing multioperator, measure of noncompactness, fixed point

 Funding Agency Grant Number Russian Foundation for Basic Research 20-51-15003 Ministry of Science and Higher Education of the Russian Federation ÌÊ-338.2021.1.1 The work of the first and second authors was supported by the Russian Foundation for Basic Research (project no. 20-51-15003-ÍÖÍÈ_à). The work of the third author was supported by the grant from the President of the Russian Federation for young scientists - candidates of science (project no. ÌÊ-338.2021.1.1).

DOI: https://doi.org/10.20310/2686-9667-2021-26-135-250-270

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UDC: 517.927.21

Citation: M. I. Kamenskii, V. V. Obukhovskii, G. Petrosyan, “On the existence of a solution for a periodic boundary value problem for semilinear fractional-order differential inclusions in Banach spaces”, Russian Universities Reports. Mathematics, 26:135 (2021), 250–270

Citation in format AMSBIB
\Bibitem{KamObuPet21} \by M.~I.~Kamenskii, V.~V.~Obukhovskii, G.~Petrosyan \paper On the existence of a solution for a periodic boundary value problem for semilinear fractional-order differential inclusions in Banach spaces \jour Russian Universities Reports. Mathematics \yr 2021 \vol 26 \issue 135 \pages 250--270 \mathnet{http://mi.mathnet.ru/vtamu230} \crossref{https://doi.org/10.20310/2686-9667-2021-26-135-250-270}