  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.

Statistical Mechanics;Disordered Systems and Neural Networks;Subcellular Processes