On Fractional Analogs of Dirichlet and Neumann Problems for the Laplace Equation

被引：0
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作者：
Batirkhan Turmetov
Kulzina Nazarova
机构：
[1] Ahmet Yesevi University,
来源：
Mediterranean Journal of Mathematics | 2019年 / 16卷
关键词：
Laplace equation; Dirichlet problem; Neumann problem; Fractional derivative; Riemann–Liouville operator; Caputo operator; uniqueness; existence; Primary 31A05; Secondary 35J05;
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摘要：
In this paper, we investigate solvability of fractional analogs of the Dirichlet and Neumann boundary-value problems for the Laplace equation. Operators of fractional differentiation in the Riemann–Liouville and Caputo sense are considered as boundary operators. The considered problems are solved by reducing them to Fredholm integral equations. Theorems on existence and uniqueness of solutions of the problems are proved.
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