Earlier we considered the use of the apparatus of fractional derivatives to solve the two-dimensional 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 nu = 0.5 and for fractional values of the interval nu is an element of [0, 1], the general solution will be investigated numerically.