On the solvability of some boundary value problems for the Poisson equation

Abstract

This work is devoted to the study of the solvability of some boundary value problems for the Poisson equation. Boundary operators are defined using fractional derivatives. The problems under consideration generalize the well-known Dirichlet and Neumann problems for the Poisson equation. The problems under study are solved by using operator methods. In the article solutions of the considered problems are determined and their uniqueness is proved.