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Application of Fractional Differential Equations in Modelling the Subdiffusion–Reaction Process

Published online by Cambridge University Press:  24 April 2013

T. Kosztołowicz  and
K. D. Lewandowska
T. Kosztołowicz*
Affiliation:
Institute of Physics, Jan Kochanowski University, ul. Świętokrzyska 15, 25-406 Kielce, Poland
K. D. Lewandowska
Affiliation:
Department of Radiological Informatics and Statistics, Medical University of Gdańsk, ul. Tuwima 15, 80-210 Gdańsk, Poland
*
⋆ Corresponding author. E-mail: tadeusz.kosztolowicz@ujk.edu.pl
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Abstract

We focus on a subdiffusion–reaction system in which substances are separated at the initial moment. This system is described by nonlinear differential subdiffusion–reaction equations with a fractional time derivative. These equations are very difficult to solve but there exist methods which allow us to solve them approximately. We discuss how useful such methods are, in particular, the quasistatic approximation method and the perturbation method in analytical solving subdiffusion–reaction equations.

Keywords

nonlinear fractional differential equationsnumerical calculationsanomalous diffusion
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 2: Anomalous diffusion , 2013 , pp. 44 - 54
Copyright
© EDP Sciences, 2013

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