Fractional diffusion equations and applications

Abstract

This paper presents a method for an explicit analysis of the equations with fractional derivatives that describe important physical processes in solar wind plasmas, in plasmas of thermonuclear devices, etc. Space‐time fractional diffusions account for anomalous features, which are observed in such physical processes. In certain cases the fundamental solutions of these equations can be interpreted as probability density functions. Thus, we observe that anomalous diffusion equations are related to Levy stable non‐Gaussian processes. An example is the multiscale nature of the magnetosphere, where the correlated data of the solar wind‐magnetosphere system show that probability distribution function is non‐Gaussian.