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Bulletin of Irkutsk State University. Series Mathematics, 2021, Volume 35, Pages 34–48
DOI: https://doi.org/10.26516/1997-7670.2021.35.34 (Mi iigum442) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Integro-differential equations and functional analysis

An initial problem for a class of weakly degenerate semilinear equations with lower order fractional derivatives

G. D. Baybulatovaa, M. V. Plekhanovaab

a Chelyabinsk State University, Chelyabinsk, Russian Federation
b South Ural State University (National Research University), Chelyabinsk, Russian Federation
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DOI: https://doi.org/10.26516/1997-7670.2021.35.34
Abstract: An initial value problem is studied for a class of evolutionary equations with a weak degeneration, which are nonlinear with respect to lower order fractional Gerasimov – Caputo derivatives. The linear part of the equations contains a respectively bounded pair of operators. Unique local solvability is proved in the case of a nonlinear operator depending on elements of the degeneration space only. Examples of an equation and a system of partial differential equations are given, the initial-boundary value problems for which are reduced to the initial problem for an equation in a Banach space of the studied class.
Keywords: fractional Gerasimov – Caputo derivative, fractional order differential equation, degenerate evolution equation, semilinear equation.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 02.A03.21.0011
Russian Foundation for Basic Research 20-31-90015
21-51-54003
The reported study was funded by Act 211 of Government of the Russian Federation, contract 02.A03.21.0011; and by the Russian Foundation for Basic Research, project numbers 20-31-90015 and 21-51-54003.
Received: 31.01.2021
Bibliographic databases:
Document Type: Article
UDC: 518.517
MSC: 03C07, 03C60
Language: English
Citation: G. D. Baybulatova, M. V. Plekhanova, “An initial problem for a class of weakly degenerate semilinear equations with lower order fractional derivatives”, Bulletin of Irkutsk State University. Series Mathematics, 35 (2021), 34–48
Citation in format AMSBIB
\Bibitem{BayPle21}
\by G.~D.~Baybulatova, M.~V.~Plekhanova
\paper An initial problem for a class of weakly degenerate semilinear equations with lower order fractional derivatives
\jour Bulletin of Irkutsk State University. Series Mathematics
\yr 2021
\vol 35
\pages 34--48
\mathnet{http://mi.mathnet.ru/iigum442}
\crossref{https://doi.org/10.26516/1997-7670.2021.35.34}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000629260200003}
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    • This publication is cited in the following 1 articles:
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