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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2022, Number 9, Pages 83–94
DOI: https://doi.org/10.26907/0021-3446-2022-9-83-94 (Mi ivm9814) 		 
This article is cited in 3 scientific papers (total in 3 papers)

The Dirichlet Problem for a mixed-type equation with fractional derivatives

K. B. Sabitovab

a Institute of strategic researches of the Republic of Bashkortostan, 15 Kirova str., Ufa, 450077 Russia
b Sterlitamak branch of Bashkir State University, 37 Lenina Ave., Sterlitamak, 453126 Russia
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DOI: https://doi.org/10.26907/0021-3446-2022-9-83-94
Abstract: In this paper we study the first boundary value problem for equation of mixed type with fractional derivatives in a rectangular domain. The criterion for the uniqueness of the solution of the problem is established. The solution is constructed as a sum of an orthogonal series and its convergence is shown in the class of regular solutions of this equations. The stability of the solution with respect to given boundary functions is established in the class of continuous and square-summable functions.
Keywords: the mixed-type equation with fractional derivatives, the Dirichlet problem, criterion of uniqueness, existence, series, stability.
Received: 05.11.2021
Revised: 10.02.2022
Accepted: 08.04.2022
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2022, Volume 66, Issue 9, Pages 71–81
DOI: https://doi.org/10.3103/S1066369X22090080
Document Type: Article
UDC: 517.95
Language: Russian
Citation: K. B. Sabitov, “The Dirichlet Problem for a mixed-type equation with fractional derivatives”, Izv. Vyssh. Uchebn. Zaved. Mat., 2022, no. 9, 83–94; Russian Math. (Iz. VUZ), 66:9 (2022), 71–81
Citation in format AMSBIB
\Bibitem{Sab22}
\by K.~B.~Sabitov
\paper The Dirichlet Problem for a mixed-type equation with fractional derivatives
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2022
\issue 9
\pages 83--94
\mathnet{http://mi.mathnet.ru/ivm9814}
\crossref{https://doi.org/10.26907/0021-3446-2022-9-83-94}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2022
\vol 66
\issue 9
\pages 71--81
\crossref{https://doi.org/10.3103/S1066369X22090080}
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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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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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