RT Journal Article
SR Electronic
A1 Kisela, Tomas
T1 Applications of the Fractional Calculus: On a Discretization of Fractional Diffusion Equation in One Dimension
JF Communications - Scientific Letters of the University of Zilina
YR 2010
VO 12
IS 1
SP 5
OP 11
DO 10.26552/com.C.2010.1.5-11
UL https://komunikacie.uniza.sk/artkey/csl-201001-0001.php
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.