On one mathematical model of substance transfer in fractal media

Qualitatively new mathematical model of finite-size waves propagation in semi-boundless channel filled with liquid or gas and having flat parallel walls, which are surrounded by fractal media. For this model, which is a one-dimensional wave equation with fractional sum of $3/2$ order, existence of singular solution is proved. Co-structural form of this solution is established by Fourier method. Solution of Cauchy problem for this model is found by integral equations method for the case when the speed of filtration changes according to law which considers the effects of the filtration processes in fractal media.