New York Journal of Mathematics
Volume 20 (2014) 1237-1251


B. Kh. Turmetov and B. T. Torebek

On solvability of some boundary value problems for a fractional analogue of the Helmholtz equation

view    print

Published: December 7, 2014
Keywords: Riemann-Liouville operator, Caputo operator, sequential derivative, Helmholtz equation, Laplace operator, fractional differential equation, Mittag-Leffler function, boundary value problem.
Subject: 34A08, 35R11, 74S25

In this paper we study some boundary value problems for fractional analogue of Helmholtz equation in a rectangular and in a half-band. Theorems about existence and uniqueness of a solution of the considered problems are proved by spectral method.

Author information

B. Kh. Turmetov:
B.Sattarkhanov street, 29, 161200, Department of Mathematics, Akhmet Yasawi International Kazakh-Turkish University, Kazakhstan, Turkistan

B. T. Torebek:
A.Pushkin street, 125, 050010, Institute of Mathematics and Mathematical Modelling MES RK, Kazakhstan, Almaty