Scattering of a Cylindrical Wave from an Impedance Strip by Using the Method of Fractional Derivatives

Abstract

Earlier, we considered the use of fractional derivative approach to solve two dimensional diffraction problems with incoming wave as plane wave or cylindrical wave on an impedance strip. By introducing the fractional boundary condition (FBC), the "fractional strip" which is subject to FBC is solved. FBC acts as an intermediate case between perfect electric conductor and perfect magnetic conductor. The Cylindrical wave diffraction problem from a strip described by FBC is formulated and solved using new method. While analyzing the scattering properties of fractional strip, new features are observed. When fractional order (FO) equals to 0.5, the problem can be found in analytical form for any value of wavenumber. Here, FO is taken 0.5 and the study is done by putting line source at far field and having analytical solution by using asymptotic approach.