On one generalization of the Neumann problem for the Laplace equation

2018

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DOI 10.1063/1.5049047
Data confidence 70 medium
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Abstract

In the paper we investigate solvability of a fractional analogue of the Neumann problem for the Laplace equation. As a boundary operator we consider operators of fractional differentiation in the Hadamard sense. The problem is solved by reduction to the integral Fredholm equation. Theorem on existence and uniqueness of the problem solution is proved.