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arXiv · 1902.03087

Asymptotic behavior of the solution of the space dependent variable order fractional diffusion equation: ultra-slow anomalous aggregation

Sergei Fedotov·Daniel Han
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Abstract

We find for the first time the asymptotic representation of the solution to the space dependent variable order fractional diffusion and Fokker-Planck equations. We identify a new advection term that causes ultra-slow spatial aggregation of subdiffusive particles due to dominance over the standard advection and diffusion terms, in the long-time limit. This uncovers the anomalous mechanism by which non-uniform distributions can occur. We perform experiments on intracellular lysosomal distributions and Monte Carlo simulations and find excellent agreement between the asymptotic solution, particle histograms and experiments.

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BibTeXRIS

Sergei Fedotov, Daniel Han. 2019-02-08. Asymptotic behavior of the solution of the space dependent variable order fractional diffusion equation: ultra-slow anomalous aggregation. https://doi.org/10.1103/physrevlett.123.050602

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