Numerical Models of Diffusion Processes Based on Fractional Order Derivatives

In the paper is considered the mathematical model of the diffusion process on the basis of the differential diffusion-advection equation with fractional order derivatives in temporal and spatial coordinates. Differences schemes for approximation of mathematical model of diffusion process with fractal structure are presented and algorithms for their realization are created. It is analysed the relationship between the density functions of the fractionally stable distributions and the solutions of the fractional equation of the diffusion process over time. Discrete random walk models based on difference algorithms are presented. On the basis of the developed software, trajectories of random walks are analysed, depending on different values of fractional derivatives.