On a generalization of the robin problem for the Laplace equation in the circle

M.E. Baltabaeva, Batirkhan Turmetov

2022

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DOI 10.47526/2022-3/2524-0080.03

Data confidence 70 medium

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Abstract

In this paper, we study the solvability of the fractional analogue of the Robin problem for the Laplace equation. A modified fractional differentiation operator in the sense of Hadamard is considered as a boundary operator. Boundary conditions are given in the form of a connection between different values of the unknown function in a circle. The problem is solved using the Fourier expansion method. For various values of the parameters of the boundary operators involved, theorems on the existence and uniqueness of a solution to the problem under study are proved.