Solvability of boundary-value problems for Poisson equations with Hadamard type boundary operator

Abstract

In this article we study properties of some integro-differential operators of fractional order. As an application of the properties of these operators for Poisson equation we examine questions on solvability of a fractional analogue of Neumann problem and analogues of periodic boundary-value problems for circular domains. The exact conditions for solvability of these problems are found.

Keywords

• Fractional derivative
• Hadamard operator
• Poisson equation
• Neumann problem