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The purpose of this work is to propose a non-Markovian and nonlinear model ofsubdiffusive transport that involves adhesion affects the cells escape ratesform position x, with chemotaxis. This leads the escape rates to be dependenton the particles density at the neighbours as well as the chemotactic gradient.We systematically derive subdiffusive fractional master equation, then weconsider the diffusive limit of the fractional master equation. We finallysolve the resulted fractional subdiffusive master equation stationery andanalyse the role of adhesion in the resulted stationary density.

A non-linear subdiffusion model for a cell-cell adhesion in chemotaxis