This paper is concerned with a non-homogeneous in space and non-local in time random walkmodel for anomalous subdiffusive transport of cells. Starting with a Markov modelinvolving a structured probability density function, we derive the non-local in timemaster equation and fractional equation for the probability of cell position. We derivethe fractional Fokker-Planck equation for the density of cells and apply this equation tothe anomalous chemotaxis problem. We show the structural instability of fractionalsubdiffusive equation with respect to the partial variations of anomalous exponent. Wefind the criteria under which the anomalous aggregation of cells takes place in thesemi-infinite domain.
