Solving boundary problems for biharmonic operator by using Integro-differential operators of fractional order

Abstract

The investigation of the properties of the integro-differential operators will be carried out. Which generalizes the well-known Bavrin operators to the fractional value of the parameters. The properties of the defined operators are in the classes of the polyharmonic operators. It is established that the newly defined fractional operators map the polyharmonic functions on the ball to the polyharmonic functions. Also it is proposed that the inverse for the fractional operator and application of the integro-differential fractional operators to solve biharmonic problems with fractional boundary conditions. The sufficient condition for existence and uniqueness of the solution for biharmonic equation with fractional boundary conditions are obtained. The solution of the biharmonic equation is obtained by using the integro-differential fractional operator.