| Issue |
Math. Model. Nat. Phenom.
Volume 8, Number 2, 2013
Anomalous diffusion
|
|
|---|---|---|
| Page(s) | 44 - 54 | |
| DOI | https://doi.org/10.1051/mmnp/20138204 | |
| Published online | 24 April 2013 | |
Application of Fractional Differential Equations in Modelling the Subdiffusion–Reaction Process
1 Institute of Physics, Jan Kochanowski
University, ul. Świętokrzyska
15, 25-406
Kielce,
Poland
2 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
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.
Mathematics Subject Classification: 35R11 / 35K57 / 82B80
Key words: nonlinear fractional differential equations / numerical calculations / anomalous diffusion
© EDP Sciences, 2013
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