This article is cited in 5 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. Durdiev<sup>ab

a</sup> Bukhara Branch of Institute of Mathematics at the Academy of Sciences of Uzbekistan, Bukhara, 705018, Uzbekistan
^b Bukhara State University, Bukhara, 705018, Uzbekistan

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.

UDC: 517.956.6

MSC: 35K15, 35R30, 35R09

Received: April 25, 2022
Revised: May 27, 2022
Accepted: June 7, 2022
First online: June 30, 2022

Language: English

DOI: 10.14498/vsgtu1921

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