Nonstationary reflections of waves in media with fractal dispersion

Numerical and analytical solutions to the problem of wave reflection in a one-dimensional medium with fractal frequency dispersion have been obtained by using the invariant-immersion method with the multiple-scattering and long-term-memory effects taken into account. As the characteristics of the medium, the solutions to the equations of the fractional relaxator and oscillator are used. The specific features of the reflections are considered for various fractal-dispersion properties. The applicability of the obtained solutions to the diagnostic of dielectrics, plasma, and elastic bodies is discussed.