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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
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.
Received: 31.01.2021
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
Linking options:
https://www.mathnet.ru/eng/iigum442 https://www.mathnet.ru/eng/iigum/v35/p34
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