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 @a-stable Levy distribution, 0<@a<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.

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