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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 4 scientific papers (total in 4 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
Full-text PDF (909 kB) Citations (4)
(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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  • https://www.mathnet.ru/eng/vsgtu1921
  • https://www.mathnet.ru/eng/vsgtu/v226/i2/p355
    • This publication is cited in the following 4 articles:
    1. D. K. Durdiev, T. R. Suyarov, Kh. Kh. Turdiev, “Obratnaya koeffitsientnaya zadacha dlya drobnogo telegrafnogo uravneniya s sootvetstvuyuschei drobnoi proizvodnoi po vremeni”, Izv. vuzov. Matem., 2025, no. 2, 39–52  mathnet  crossref
    2. Askar Rahmonov, Durdimurod Durdiev, Dilshoda Akramova, PROBLEMS IN THE TEXTILE AND LIGHT INDUSTRY IN THE CONTEXT OF INTEGRATION OF SCIENCE AND INDUSTRY AND WAYS TO SOLVE THEM: PTLICISIWS-2, 3045, PROBLEMS IN THE TEXTILE AND LIGHT INDUSTRY IN THE CONTEXT OF INTEGRATION OF SCIENCE AND INDUSTRY AND WAYS TO SOLVE THEM: PTLICISIWS-2, 2024, 040012  crossref
    3. D. K. Durdiev, “Unknown coefficient problem for mixed equation of parabolic-hyperbolic type with non-local boundary conditions on characteristics”, Ufa Math. J., 16:2 (2024), 81–88  mathnet  mathnet  crossref
    4. D. K. Durdiev, “Obratnaya zadacha dlya uravneniya smeshannogo parabolo-giperbolicheskogo tipa s kharakteristicheskoi liniei izmeneniya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 27:4 (2023), 607–620  mathnet  crossref
    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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