| Issue |
Math. Model. Nat. Phenom.
Volume 8, Number 2, 2013
Anomalous diffusion
|
|
|---|---|---|
| Page(s) | 28 - 43 | |
| DOI | https://doi.org/10.1051/mmnp/20138203 | |
| Published online | 24 April 2013 | |
Non-homogeneous Random Walks, Subdiffusive Migration of Cells and Anomalous Chemotaxis
1 School of Mathematics, The University
of Manchester, Manchester, M13
9PL, UK
2 Department of Mathematical Physics,
Ural Federal University, Ekaterinburg, 620083, Russia
⋆ Corresponding author. E-mail:
sergei.fedotov@manchester.ac.uk
This paper is concerned with a non-homogeneous in space and non-local in time random walk model for anomalous subdiffusive transport of cells. Starting with a Markov model involving a structured probability density function, we derive the non-local in time master equation and fractional equation for the probability of cell position. We derive the fractional Fokker-Planck equation for the density of cells and apply this equation to the anomalous chemotaxis problem. We show the structural instability of fractional subdiffusive equation with respect to the partial variations of anomalous exponent. We find the criteria under which the anomalous aggregation of cells takes place in the semi-infinite domain.
Mathematics Subject Classification: 60G22 / 82C31 / 92B05
Key words: anomalous random walks / cell migration / aggregation
© EDP Sciences, 2013
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