ON THE INVERSE PROBLEM OF THE BITSADZE–SAMARSKII TYPE FOR A FRACTIONAL PARABOLIC EQUATION

Ashurov R.R. Kadirkulov B.J. Turmetov B.Kh.
2023 Petrozavodsk State University

Problemy Analiza
2023 #12(30)Issue 3 20 - 40 pp.

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.

Hadamard–Caputo fractional operator , inverse problem , Le Roy function , Riesz basis

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Institute of Mathematics, Uzbekistan Academy of Science, University street 9, Tashkent, 100174, Uzbekistan
School of Engineering, Central Asian University, 264, Milliy Bog St., Tashkent, 111221, Uzbekistan
Tashkent State University of Oriental Studies, Amir Temur Str. 20, Tashkent, 100060, Uzbekistan
Khoja Akhmet Yassawi International Kazakh-Turkish University, Bekzat Sattarhanov ave., 29, Turkistan, 161200, Kazakhstan

Institute of Mathematics
School of Engineering
Tashkent State University of Oriental Studies
Khoja Akhmet Yassawi International Kazakh-Turkish University

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