Journal of Theoretical
and Applied Mechanics

44, 2, pp. 393-403, Warsaw 2006

Numerical solutions to boundary value problem for anomalous diffusion equation with Riesz-Feller fractional operator

Mariusz Ciesielski, Jacek Leszczynski
In this paper, we present a numerical solution to an ordinary differential equation of a fractional order in one-dimensional space. The solution to this equation can describe a steady state of the process of anomalous diffusion. The process arises from interactions within complex and non-homogeneous background. We present a numerical method which is based on the finite differences method. We consider a boundary value problem (Dirichlet conditions) for an equation with the Riesz-Feller fractional derivative. In the final part of this paper, some simulation results are shown. We present an example of non-linear temperature profiles in nanotubes which can be approximated by a solution to the fractional differential equation.
Keywords: Riesz-Feller fractional derivative; boundary value problem; Dirichlet conditions; finite difference method