On solvability of fractional analogues of the Neumann problem for biharmonic equation

Abstract

In the paper we research the questions about solvability of some boundary value problems for biharmobic equations. As a boundary operator we consider the differentiation operator of fractional order in Miller-Ross sense. Consider properties of integral - differential operators of fractional order in the class of functions, which are smooth in the unit ball. We study properties of the solution of the Dirichlet problem for a biharmonic equation. The considered problem is a generalation of the well known Neumann problem.