Subdiffusion of Particles with a Nonlinear Interaction and Cell-Cell Adhesion

Abstract The main goal of this work is to propose a non-Markovian model for a subdiffusive transport of particles with nonlinear interaction that involves adhesion affects on escape rates from position x, in inhomogeneous media. In this case, the escape rates to be dependent on the particle density and also effected by the density at the neighbors as well as the chemotactic gradient. We systematically derive the subdiffusive fractional master equation. Considering the spatial continuum limit of the fractional master equation implies a stationary solution of the resulted fractional subdiffusive master equation. Finally, we analyze the role of adhesion in the resulted stationary density.