Simulation of the continuous time random walk of the space-fractional diffusion equations

In this article, we discuss the solution of the space-fractional diffusion equation with and without central linear drift in the Fourier domain and show the strong connection between it and the alpha-stable Levy distribution, 0 < alpha < 2. We use some relevant transformations of the independent variables x and t, to find the solution of the space-fractional diffusion equation with central linear drift which is a special form of the space-fractional Fokker-Planck equation which is useful in studying the dynamic behaviour of stochastic differential equations driven by the non-Gaussian (Levy) noises. We simulate the continuous time random walk of these models by using the Monte Carlo method. (c) 2007 Elsevier B.V. All rights reserved.