Asymptotic behavior of the solution of the space dependent variable order fractional diffusion equation: ultra-slow anomalous aggregation
2019
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 good agreement between the asymptotic solution, particle histograms and experiments.
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