PT  - JOURNAL ARTICLE
AU  - Kisela, Tomas
TI  - Applications of the Fractional Calculus: On a Discretization of Fractional Diffusion Equation in One Dimension
DP  - 2010 Mar 31
TA  - Communications - Scientific Letters of the University of Zilina
PG  - 5--11
VI  - 12
IP  - 1
AID - 10.26552/com.C.2010.1.5-11
IS  - 13354205
AB  - 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.