MATHEMATICS

Inverse coefficient problem for a partial differential equation with multi-term orders fractional Riemann–Liouville derivatives

D. K. Durdiev^a, I. I. Hasanov<sup>b

a</sup> Bukhara Branch of the Institute of Mathematics named after V. I. Romanovskiy at the Academy of Sciences of the Republic of Uzbekistan, ul. M. Iqbol, 11, Bukhara, 200118, Uzbekistan
^b Bukhara State University, ul. M. Iqbol, 11, Bukhara, 200118, Uzbekistan

Abstract: This work studies direct initial boundary value and inverse coefficient determination problems for a one-dimensional partial differential equation with multi-term orders fractional Riemann–Liouville derivatives. The unique solvability of the direct problem is investigated and a priori estimates for its solution are obtained in weighted spaces, which will be used for studying the inverse problem. Then, the inverse problem is equivalently reduced to a nonlinear integral equation. The fixed-point principle is used to prove the unique solvability of this equation.

Keywords: fractional order equation, direct problem, inverse problem, Fourier method, Mittag–Leffler function, Laplace transform, existence, uniqueness

UDC: 517.958

MSC: 35K20, 35R09, 35R30

Received: 03.04.2024
Accepted: 21.08.2024

Language: English

DOI: 10.35634/vm240302

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