  In this paper, we formulate the space-dependent variable-order fractional
master equation to model clustering of particles, organelles, inside living
cells. We find its solution in the long time limit describing non-uniform
distribution due to a space dependent fractional exponent. In the continuous
space limit, the solution of this fractional master equation is found to be
exactly the same as the space-dependent variable-order fractional diffusion
equation. In addition, we show that the clustering of lysosomes, an essential
organelle for healthy functioning of mammalian cells, exhibit space-dependent
fractional exponents. Furthermore, we demonstrate that the non-uniform
distribution of lysosomes in living cells is accurately described by the
asymptotic solution of the space-dependent variable-order fractional master
equation. Finally, Monte Carlo simulations of the fractional master equation
validate our analytical solution.
