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

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.

arXiv comment6 pages

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Cited by in corpus (10)

• Variable-order fractional calculus: a change of perspective
• Fractional advection-diffusion-asymmetry equation
• Subdiffusion equation with Caputo fractional derivative with respect to another function
• Local Analysis of Heterogeneous Intracellular Transport: Slow and Fast moving Endosomes
• Subdiffusion equation with fractional Caputo time derivative with respect to another function in modeling transition from ordinary subdiffusion to superdiffusion
• Population heterogeneity in the fractional master equation, ensemble self-reinforcement and strong memory effects
• Variable-order fractional master equation and clustering of particles: non-uniform lysosome distribution
• Inhomogeneous parametric scaling and variable-order fractional diffusion equations
• Unravelling Heterogeneous Transport of Endosomes
• An Adaptive Difference Method for Variable-Order Diffusion Equations