MATHEMATICS

Boundary value problem for the loaded fractional telegraph equation with Gerasimov–Caputo derivatives

F. M. Losanova, R. O. Kenetova

Institute of Applied Mathematics and Automation, Nalchik

Abstract: The first boundary value problem in the rectangular region for the loaded fractional telegraph equation with Gerasimov–Caputo derivatives is investigated. By the method of reduction to the Volterra integral equation of the 2nd kind the solution of the problem is found. The existence and uniqueness theorem of the solution is proved.

Keywords: first boundary value problem, loaded fractional telegraph equation, Gerasimov–Caputo derivative, Green’s function, Wright’s function.

UDC: 517.95

MSC: 35A08, 35A09, 34A08

Received: 06.12.2024
Revised: 13.12.2024
Accepted: 16.12.2024

DOI: 10.47928/1726-9946-2024-24-4-39-46

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