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

Mariusz Ciesielski·Jacek Leszczynski
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Abstract

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, same 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.

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Mariusz Ciesielski, Jacek Leszczynski. 2006-07-05. Numerical solutions to boundary value problem for anomalous diffusion equation with Riesz-Feller fractional operator. https://arxiv.org/abs/math/0607140

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