Applying fractional calculus in models of anomalous diffusion

Аuthors

Reviznikov D. L.^*, Slastushenskiy Y. V.^**

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: reviznikov@inbox.ru
**e-mail: v_slastushensky@mosinter.net

Abstract

Some problems of applying fractional calculus in models of anomalous diffusion are considered. High order finite-difference methods are presented for the anomalous diffusion equation with fractional derivatives in time and space. A random walk model for this equation is proposed. It is shown that results of numerical solution obtained with different methods are in good agreement.

Keywords:

fractional calculus; anomalous diffusion; fractional derivative; Granwald-Letnikov formula; finite-difference scheme; Runge-Romberg-Richardson method; random walk model; Monte-Carlo method.