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Chelyabinskiy Fiziko-Matematicheskiy Zhurnal, 2022, Volume 7, Issue 1, Pages 11–19
DOI: https://doi.org/10.47475/2500-0101-2022-17101 (Mi chfmj267) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Mathematics

On solvability of some classes of equations with Hilfer derivative in Banach spaces

A. R. Volkovaa, V. E. Fedorova, D. M. Gordievskikhb

a Chelyabinsk State University, Chelyabinsk, Russia
b Shadrinsk State Pedagogical University, Shadrinsk, Russia
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DOI: https://doi.org/10.47475/2500-0101-2022-17101
Abstract: The issues of unique solvability of a Cauchy-type problem for an evolutionary equation in a Banach space with a Hilfer fractional derivative and with a bounded operator are investigated. The existence of a unique solution to the problem is proved, the solution is presented using Mittag-Leffler operator functions. The abstract result is used when considering a class of initial boundary value problems for partial differential equations
Keywords: Hilfer derivative, fractional order equation, initial problem, theorem on the existence and uniqueness of a solution, linear inhomogeneous equation, initial boundary value problem, Laplace operator.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation НШ-2708.2022.1.1
The work of A.R.V. was funded by a grant of the President of the Russian Federation for state support of leading scientific schools NSH-2708.2022.1.1, the work of V.E.F. and D.M.G. was supported by the Bashkir State Pedagogical University named after M. Akmulla, contract no. 775 EP dated 01.12.2021.
Received: 22.10.2021
Revised: 16.12.2021
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: A. R. Volkova, V. E. Fedorov, D. M. Gordievskikh, “On solvability of some classes of equations with Hilfer derivative in Banach spaces”, Chelyab. Fiz.-Mat. Zh., 7:1 (2022), 11–19
Citation in format AMSBIB
\Bibitem{VolFedGor22}
\by A.~R.~Volkova, V.~E.~Fedorov, D.~M.~Gordievskikh
\paper On solvability of some classes of equations with Hilfer derivative in Banach spaces
\jour Chelyab. Fiz.-Mat. Zh.
\yr 2022
\vol 7
\issue 1
\pages 11--19
\mathnet{http://mi.mathnet.ru/chfmj267}
\crossref{https://doi.org/10.47475/2500-0101-2022-17101}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4409128}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Chelyabinskiy Fiziko-Matematicheskiy Zhurnal
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