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On solvability of a nonlocal problem for the Laplace equation with the fractional-order boundary operator

Moldir A Muratbekova*, Kanat M Shinaliyev and Batirkhan K Turmetov

Author Affiliations

Department of Mathematics, Akhmet Yasawi International Kazakh-Turkish University, B. Sattarkhanov Street 29, Turkistan, 161200, Kazakhstan

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Boundary Value Problems 2014, 2014:29  doi:10.1186/1687-2770-2014-29

Published: 30 January 2014

Abstract

In the present work, we study properties of some integro-differential operators of the Hadamard-Marchaud type in the class of harmonic functions. As an application of these properties, we consider the question of the solvability of a nonlocal boundary value problem for the Laplace equation in the unit ball.

MSC: 35J05, 35J25, 26A33.

Keywords:
Hadamard-Marchaud operator; fractional derivative; nonlocal problem