Applications of the Fractional Calculus: On a Discretization of Fractional Diffusion Equation in One Dimension
Applications of the Fractional Calculus: On a Discretization of Fractional Diffusion Equation in One Dimension

Summary/Abstract: The paper discusses the problem of classical and fractional diffusion models. It is known that the classical model fails in heterogeneous structures with locations where particles move at a large speed over a long distance. If we replace the second derivative in the space variable in the classical diffusion equation by a fractional derivative of order less than two, we obtain the fractional diffusion equation (FDE) which is more useful in this case. In this paper we introduce a discretization of FDE based on the theory of the difference fractional calculus and we sketch a basic numerical scheme of its solution. Finally, we present some examples comparing classical and fractional diffusion models.

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