Numerical treatment of an initial-boundary value problem for fractional partial differential equations

Authors:
Mariusz Ciesielski;Jacek Leszczynski
Affiliations:
Institute of Mathematics and Computer Science, Czestochowa University of Technology, Czestochowa, Poland;Institute of Mathematics and Computer Science, Czestochowa University of Technology, Czestochowa, Poland
Venue:
Signal Processing - Fractional calculus applications in signals and systems
Year:
2006

Citing 2
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Abstract

This paper deals with numerical solutions to a partial differential equation of fractional order. Generally this type of equation describes a transition from anomalous diffusion to transport processes. From a phenomenological point of view, the equation includes at least two fractional derivatives: spatial and temporal. In this paper we proposed a new numerical scheme for the spatial derivative, the so-called Riesz-Feller operator. Moreover, using the finite difference method, we show how to employ this scheme in the numerical solution of fractional partial differential equations. In other words, we considered an initial-boundary value problem in one-dimensional space. In the final part of this paper some numerical results and plots of simulations are shown as examples.