  We show how the nonlinear interaction effects `volume filling' and `adhesion'
can be incorporated into the fractional subdiffusive transport of cells and
individual organisms. To this end, we use microscopic random walk models with
anomalous trapping and systematically derive generic non-Markovian and
nonlinear governing equations for the mean concentrations of the subdiffusive
cells or organisms. We uncover an interesting interaction between the
nonlinearities and the non-Markovian nature of the transport. In the
subdiffusive case, this interaction manifests itself in a nontrivial
combination of nonlinear terms with fractional derivatives. In the long time
limit, however, these equations simplify to a form without fractional
operators. This provides an easy method for the study of aggregation phenomena.
In particular, this enables us to show that volume filling can prevent
"anomalous aggregation," which occurs in subdiffusive systems with a spatially
varying anomalous exponent.
