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 Ufimsk. Mat. Zh., 2020, Volume 12, Issue 3, Pages 71–82 (Mi ufa529)

On antiperiodic boundary value problem for semilinear fractional differential inclusion with deviating argument in Banach space

G. G. Petrosyan

Voronezh State University of Engineering Technologies, Revolutsii av. 19, 394036, Voronezh, Russia

Abstract: We consider a boundary value problem for a semi-linear differential inclusion of Caputo fractional derivative and a deviating coefficient in a Banach space. We assume that the linear part of the inclusion generates a bounded $C_0$-semigroup. A nonlinear part of the inclusion is a multi-valued mapping depending on the time and the prehistory of the function before a current time. The boundary condition is functional and anti-periodic in the sense that one function is equals to another with an opposite sign. To solve the considered problem, we employ the theory of fractional mathematical analysis, the properties of Mittag-Leffler as well as the theory of topological power for multi-valued condensing maps. The idea is as follws: the original problem is reduced to the existence of fixed points of a corresponding resolving multi-valued integral operator in the space of continuous functions. To prove the existence of the fixed points of the resolving multi-operator we employ a generalized theorem of Sadovskii type on a fixed point. This is why we show that the resolving integral multi-operator is condensing with respect to a vector measure of non-compactness in the space of continuous functions and maps a closed ball in this space into itself.

Keywords: Caputo fractional derivative, semi-linear differential inclusion, boundary value problem, fixed point, condensing multi-mapping, measure of non-compactness.

 Funding Agency Grant Number Russian Foundation for Basic Research 19-31-60011 The reported study was funded by RFBR according to the research project no. 19-31-60011.

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English version:
Ufa Mathematical Journal, 2020, 12:3, 69–80 (PDF, 370 kB); https://doi.org/10.13108/2020-12-3-69

Bibliographic databases:

UDC: 517.929
MSC: 34G25, 34K09, 34K37, 47H04, 47H08, 47H10

Citation: G. G. Petrosyan, “On antiperiodic boundary value problem for semilinear fractional differential inclusion with deviating argument in Banach space”, Ufimsk. Mat. Zh., 12:3 (2020), 71–82; Ufa Math. J., 12:3 (2020), 69–80

Citation in format AMSBIB
\Bibitem{Pet20} \by G.~G.~Petrosyan \paper On antiperiodic boundary value problem for semilinear fractional differential inclusion with deviating argument in Banach space \jour Ufimsk. Mat. Zh. \yr 2020 \vol 12 \issue 3 \pages 71--82 \mathnet{http://mi.mathnet.ru/ufa529} \transl \jour Ufa Math. J. \yr 2020 \vol 12 \issue 3 \pages 69--80 \crossref{https://doi.org/10.13108/2020-12-3-69} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000607973900008} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85097538469} 

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