Geodesic
On the inverse problem of the Bitsadze--Samarskii type for a fractional parabolic equation
Problemy analiza, Tome 12 (2023) no. 3, pp. 20-40

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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. 
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     title = {On the inverse problem of the {Bitsadze--Samarskii} type for a fractional parabolic equation},
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R. R. Ashurov; B. J. Kadirkulov; B. Kh. Turmetov. On the inverse problem of the Bitsadze--Samarskii type for a fractional parabolic equation. Problemy analiza, Tome 12 (2023) no. 3, pp. 20-40. http://geodesic.mathdoc.fr/item/PA_2023_12_3_a1/