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An inverse coefficient problem for the fractional telegraph equation with the corresponding fractional derivative in time
https://doi.org/10.26907/0021-3446-2025-2-39-52
Abstract
This work investigates an initial-boundary value and an inverse coefficient problem of determining a time dependent coefficient in the fractional wave equation with the conformable fractional derivative and an integral. In the beginning, the initial boundary value problem (direct problem) is considered. By the Fourier method this problem is reduced to equivalent integral equations. Then, using the technique of estimating these functions and the generalized Gronwall inequality, we get apriori estimate for the solution via the unknown coefficient which will be used to study the inverse problem. The inverse problem is reduced to an equivalent integral equation of Volterra type. To show the existence and uniqueness of the solution to this equation, the Banach principle is applied. The local existence and uniqueness results are obtained.
About the Authors
D. K. Durdiev
V.I. Romanovskiy Institute of Mathematics Uzbekistan Academy of Sciences; Bukhara State University
Uzbekistan
Uzbekistan
Durdimurod K. Durdiev.
9 University str., Tashkent, 100174; 11 M. Ikbal str., Bukhara, 200117
T. R. Suyarov
V.I. Romanovskiy Institute of Mathematics Uzbekistan Academy of Sciences; Bukhara State University
Uzbekistan
Uzbekistan
Tursunbek R. Suyarov.
9 University str., Tashkent, 100174; 11 M. Ikbal str., Bukhara, 200117
Kh. Kh. Turdiev
V.I. Romanovskiy Institute of Mathematics Uzbekistan Academy of Sciences; Bukhara State University
Uzbekistan
Uzbekistan
Khalim Kh. Turdiyev.
9 University str., Tashkent, 100174; 11 M. Ikbal str., Bukhara, 200117
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Review
For citations:
Durdiev D.K., Suyarov T.R., Turdiev Kh.Kh. An inverse coefficient problem for the fractional telegraph equation with the corresponding fractional derivative in time. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. 2025;(2):39-52. (In Russ.) https://doi.org/10.26907/0021-3446-2025-2-39-52
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