Stochastic pathway to anomalous diffusion

We present an appraisal of differential-equation models for anomalous diffusion, in which the time evolution of the mean-square displacement is 〈r²(t)〉{~}t^γ with {γ}{≠}1. By comparison, continuous-time random walks lead via generalized master equations to an integro-differential picture. Using L\'evy walks and a kernel which couples time and space, we obtain a generalized picture for anomalous transport, which provides a unified framework both for dispersive ({γ}<1) and for enhanced diffusion ({γ}>1).