Application of The Method of Fractional Derivatives to the Solution of the Problem of Plane Wave Diffraction by Two Axisymmetric Strips of Different Sizes

Abstract

In this paper, we have considered the problem of plane wave diffraction by two strips. This structure is an open resonator which consists of two axisymmetric strips of different widths. The application of the Fractional Derivative (FDM) method allows one to obtain a general solution, which, as a particular case, contains, for fractional order (FO) values α equal, α= 0 and, α= 1 the solution of the problem when the strips are perfectly electrically conductive (PEC, = 0) and perfectly magnetically conductive (PMC, α= 1). For values of the FO from the interval α ∈ (0,1), we have a resonator in which the conductivity of the mirrors is intermediate between the PEC and the PMC.