Makhmud A. Sadybekov, Batirkhan Kh. Turmetov, Berikbol T. Torebek
Abstract:
In this article, we consider a class of nonlocal problems for the Laplace
equation with boundary operators of fractional order.
We prove the existence, uniqueness and a representation of the solutions.
Also it is shown that the smoothness of solutions in Holder classes
depends on the order of the boundary operators.
Submitted March 18, 2014. Published July 10, 2014.
Math Subject Classifications: 35J15, 35J25, 34B10, 26A33, 31A05, 31B05.
Key Words: Riemann-Liouville operator; Caputo operator; periodic problem;
antiperiodic problem; nonlocal problem; Laplace equation;
Poisson kernel; harmonic function.
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Makhmud A. Sadybekov Institute of Mathematics and Mathematical Modeling Ministry of Education and Science Republic of Kazakhstan 050010 Almaty, Kazakhistan email: makhmud-s@mail.ru |
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Batirkhan Kh. Turmetov Department of Mathematics Akhmet Yasawi International Kazakh-Turkish University 161200 Turkistan, Kazakhistan email: batirkhan.turmetov@iktu.kz |
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Berikbol T. Torebek Department of Mathematics Akhmet Yasawi International Kazakh-Turkish University 161200 Turkistan, Kazakhistan email: turebekb85@mail.ru |
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