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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2022, Volume 26, Number 2, Pages 355–367
DOI: https://doi.org/10.14498/vsgtu1921 (Mi vsgtu1921) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Short Communication
Differential Equations and Mathematical Physics

Inverse source problem for an equation of mixed parabolic-hyperbolic type with the time fractional derivative in a cylindrical domain

D. K. Durdievab

a Bukhara Branch of Institute of Mathematics at the Academy of Sciences of Uzbekistan, Bukhara, 705018, Uzbekistan
b Bukhara State University, Bukhara, 705018, Uzbekistan
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(published under the terms of the Creative Commons Attribution 4.0 International License)
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DOI: https://doi.org/10.14498/vsgtu1921
Abstract: This article is devoted to the study of an inverse source problem for a mixed type equation with a fractional diffusion equation in the parabolic part and a wave equation in the hyperbolic part of a cylindrical domain. The solution is obtained in the form of Fourier–Bessel series expansion using an orthogonal set of Bessel functions. The theorems of uniqueness and existence of a solution are proved.
Keywords: inverse problem, equation of mixed type, Fourier–Bessel series, Mittag–Leffler function, uniqueness and existence.
Received: April 25, 2022
Revised: May 27, 2022
Accepted: June 7, 2022
First online: June 30, 2022
Bibliographic databases:
Document Type: Article
UDC: 517.956.6
MSC: 35K15, 35R30, 35R09
Language: English
Citation: D. K. Durdiev, “Inverse source problem for an equation of mixed parabolic-hyperbolic type with the time fractional derivative in a cylindrical domain”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 26:2 (2022), 355–367
Citation in format AMSBIB
\Bibitem{Dur22}
\by D.~K.~Durdiev
\paper Inverse source problem for an equation of mixed parabolic-hyperbolic type with the time fractional derivative in a cylindrical domain
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2022
\vol 26
\issue 2
\pages 355--367
\mathnet{http://mi.mathnet.ru/vsgtu1921}
\crossref{https://doi.org/10.14498/vsgtu1921}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4494667}
\edn{https://elibrary.ru/TWHCKX}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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