Fractional green's function and fractional boundary conditions in diffraction of electromagnetic waves on plane screens

Proposed method to solve difference-integral equation of a special type, arising in problems of diffraction by boundaries is described by fractional boundary condition (FBC). The method is considered on two boundaries - a strip and a half-plane with FBC when the fractional order varies from 0 to 1. The proposed method is based on application of orthogonal polynomials. Gegenbauer polynomials orthogonal on interval (-1,1) are utilized for a strip, while Lager polynomials orthogonal on interval (0, ∞) are used for a half-plane. One important feature of the considered integral equations is noted: these equations can be solved analytically for one special intermediate value of the fractional order (FO) α = 0, 5 and it can be done for any value of the frequency.