B. Yu. Irgashev, “A boundary value problem with conjugation conditions for a degenerate the equations with the Caputo fractional derivative”, Izv. Vyssh. Uchebn. Zaved. Mat., 2022, Number 4,Pages <nobr>27

This article is cited in 4 papers

A boundary value problem with conjugation conditions for a degenerate the equations with the Caputo fractional derivative

B. Yu. Irgashev^ab

^a Namangan Engineering Construction Institute, 12 Islam Karimov str., Namangan, 160103 Republic of Uzbekistan
^b Institute of Mathematics named after V.I. Romanovsky, 46 University str., Tashkent, 100174, Republic of Uzbekistan

Abstract: In this paper, for a degenerate higher-order equation with a fractional derivative in the sense of Caputo, a nonlocal problem with conjugation conditions in a rectangular domain is studied. The solution is constructed in the form of a Fourier series in the eigenfunctions of a one-dimensional problem. A criterion for the uniqueness of a solution is given.

Keywords: even order equation, fractional Caputo derivative, degeneration, conjugation conditions, eigenvalue, eigenfunction, Fourier series, convergence.

UDC: 517.954: 517.927: 517.589

Received: 29.06.2021
Revised: 29.06.2021
Accepted: 29.09.2021

DOI: 10.26907/0021-3446-2022-4-27-36