This article is cited in 2 papers

MATHEMATICS

Boundary value problem for a degenerate equation with a Riemann–Liouville operator

Bakhrom Yu. Irgashev<sup>ab

a</sup> Namangan Engineering Construction Institute, Namangan, Uzbekistan
^b Institute of Mathematics named after V. I. Romanovsky of the Academy of Sciences of the Republic of Uzbekistan, Uzbekistan

Abstract: In the article, the uniqueness and solvability of one boundary value problem for a high-order equation with two lines of degeneracy with a fractional Riemann–Liouville derivative in a rectangular domain is studied by the Fourier method. Sufficient conditions for the well-posedness of the problem posed are obtained.

Keywords: high order equation, initial-boundary value problem, fractional derivative in the sense of Riemann–Liouville, eigenvalue, eigenfunction, Kilbas–Saigo function, series, convergence, existence, uniqueness.

Received: 21.06.2023
Revised: 08.08.2023
Accepted: 09.09.2023

Language: English

DOI: 10.17586/2220-8054-2023-14-5-511-517

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