LAUSR

Earlier we considered the use of the apparatus of fractional derivatives to solve the twodimensional problem of diffraction of a plane wave on an impedance strip. We introduced the concept of a “fractional strip”. A “fractional strip” is understood as a strip on the surface, which is subject to fractional boundary conditions (FBC). The problem under consideration on the basis of various methods has been studied quite well. As a rule, this problem is studied on the basis of numerical methods. The proposed approach, as will be shown below, makes it possible to obtain an analytical solution of the problem for values of fractional order ν = 0.5 and for fractional values of the interval ν ∈ [0, 1], the general solution will be investigated numerically. 1. FORMULATION OF THE PROBLEM We arrange a two-dimensional strip of width 2a on the plane y = 0. The strip along the z-axis is infinite. The source of the cylindrical wave Je = zJeδ(x−xo)δ(y−yo) is located at the point (xo, yo) (see Fig. 1). Figure 1. Geometry of the problem. Let us consider the case of an E-polarized wave, i.e., Ei z(0, 0, Ez), H i z(Hx,Hy, 0). In this case, the source field has the form E z (x, y) = − Je η0k 4 H (1) 0 ( k √ (x − xo) + (y − yo) ) (1) Received 22 March 2018, Accepted 28 May 2018, Scheduled 13 June 2018 * Corresponding author: Kamil Karaçuha ([email protected]). 1 Information Institute of Istanbul Technical University, Istanbul, Turkey. 2 National Technical University ‘Kharkiv Polytechnic Institute’, Kharkiv, Ukraine.