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Problemy Analiza — Issues of Analysis, 2023, Volume 12(30), Issue 3, Pages 20–40
DOI: https://doi.org/10.15393/j3.art.2023.14370 (Mi pa381) 		 
On the inverse problem of the Bitsadze–Samarskii type for a fractional parabolic equation

R. R. Ashurovab, B. J. Kadirkulovc, B. Kh. Turmetovd

a Institute of Mathematics, Uzbekistan Academy of Science, University street 9, Tashkent, 100174, Uzbekistan
b School of Engineering, Central Asian University, 264, Milliy Bog St., 111221, Tashkent, Uzbekistan
c Tashkent State University of Oriental Studies, Amir Temur Str. 20, Tashkent,100060, Uzbekistan
d Khoja Akhmet Yassawi International Kazakh-Turkish University, Bekzat Sattarhanov ave., 29, Turkistan, 161200, Kazakhstan
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DOI: https://doi.org/10.15393/j3.art.2023.14370
Abstract: In this paper, the inverse problem of the Bitsadze–Samarsky type is studied for a fractional order equation with a Hadamard–Caputo fractional differentiation operator. The problem is solved using the spectral method. The spectral aspects of the obtained problem are investigated, root functions are found, and their basis property is proved. The conjugate problem is investigated. The uniqueness and existence theorems for a regular solution to this problem are proved.
Keywords: Hadamard–Caputo fractional operator, Riesz basis, Le Roy function, inverse problem.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan AP09259074
The research of the third author is supported by the grant of the Committee of Sciences, Ministry of Education and Science of the Republic of Kazakhstan, project AP09259074.
Received: 19.06.2023
Accepted: 10.07.2023
Document Type: Article
UDC: 517.956.42
MSC: 35K65, 34R30, 34K37, 34L10
Language: English
Citation: R. R. Ashurov, B. J. Kadirkulov, B. Kh. Turmetov, “On the inverse problem of the Bitsadze–Samarskii type for a fractional parabolic equation”, Probl. Anal. Issues Anal., 12(30):3 (2023), 20–40
Citation in format AMSBIB
\Bibitem{AshKadTur23}
\by R.~R.~Ashurov, B.~J.~Kadirkulov, B.~Kh.~Turmetov
\paper On the inverse problem of the Bitsadze--Samarskii type for a fractional parabolic equation
\jour Probl. Anal. Issues Anal.
\yr 2023
\vol 12(30)
\issue 3
\pages 20--40
\mathnet{http://mi.mathnet.ru/pa381}
\crossref{https://doi.org/10.15393/j3.art.2023.14370}
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