Models of the neutralfractional anomalous diffusion and their analysis
Abstract
Anomalous diffusion can be roughly characterized by the property that the diffusive particles do not follow the Gaussian statistics. When the mean squared displacement of the particles behaves in time like a power function, time and/or spacefractional derivatives were shown to be useful in modeling of such diffusion processes. In this paper, a special class of anomalous diffusion processes, the so called neutralfractional diffusion, is considered. The starting point is a stochastic formulation of the model in terms of the continuous time random walk processes. The neutralfractional diffusion equation in form of a partial differential equation with the fractional derivatives of the same order both in time and in space is then derived from the master equation for a special choice of the probability density functions. An explicit form of the fundamental solution of the Cauchy problem for the neutralfractional diffusion equation is presented. Its properties are studied and illustrated by plots.
 Publication:

9th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences: ICNPAA 2012
 Pub Date:
 November 2012
 DOI:
 10.1063/1.4765552
 Bibcode:
 2012AIPC.1493..626L
 Keywords:

 diffusion;
 Gaussian processes;
 master equation;
 partial differential equations;
 probability;
 random processes;
 02.30.Jr;
 02.50.r;
 02.50.Cw;
 05.40.a;
 05.60.k;
 Partial differential equations;
 Probability theory stochastic processes and statistics;
 Probability theory;
 Fluctuation phenomena random processes noise and Brownian motion;
 Transport processes