Scattering properties of the strip with fractional boundary conditions and comparison with the impedance strip

In this paper two-dimensional problem of plane-wave diffraction by a “fractional strip” is studied. “Fractional strip” is introduced as a strip with fractional boundary conditions (FBC) involving fractional derivatives of the field components. FBC describe intermediate boundary between perfect electric conductor (PEC) and perfect magnetic conductor (PMC). It is shown that “fractional strip” has scattering properties similar to the well-known impedance strip. For one important case of fractional order equal to 0.5 the solution of the wave diffraction problem by a “fractional strip” can be found analytically. Detailed comparison analysis of the physical characteristics of the scattered fields for both fractional and impedance strips is presented. The relation between the fractional order and the value of impedance is derived. It is shown that in a wide range of input parameters the physical characteristics of the “fractional strip” are similar to the strip with pure imaginary impedance.