Fractional curl operator in reflection problems

The purpose of this paper is to investigate some applications of the fractionalized curl operator in the scattering problems. Using the technique of fractionalizing a linear operator we obtain the presentation for the fractional curl operator for the functions of two variables expressed via exponents. We use this presentation in a plane wave reflection at oblique incidence on an impedance infinite surface. Applying fractional curl operator to a fixed solution we obtain the fields that describe, in certain sense, an intermediate of "fractional" solution between the original solution and its dual solution. These "fractional" fields represent the solution of reflection problem from an anisotropic surface. The relation between the impedance of such an anisotropic surface and the original impedance are presented in this paper.