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

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.