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In this paper, we formulate the space-dependent variable-order fractionalmaster equation to model clustering of particles, organelles, inside livingcells. We find its solution in the long time limit describing non-uniformdistribution due to a space dependent fractional exponent. In the continuousspace limit, the solution of this fractional master equation is found to beexactly the same as the space-dependent variable-order fractional diffusionequation. In addition, we show that the clustering of lysosomes, an essentialorganelle for healthy functioning of mammalian cells, exhibit space-dependentfractional exponents. Furthermore, we demonstrate that the non-uniformdistribution of lysosomes in living cells is accurately described by theasymptotic solution of the space-dependent variable-order fractional masterequation. Finally, Monte Carlo simulations of the fractional master equationvalidate our analytical solution.

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

Variable-order fractional master equation and clustering of particles: non-uniform lysosome distribution