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We present an appraisal of differential-equation models for anomalous diffusion, in which the time evolution of the mean-square displacement is< r 2 (t)>∼ t γ with γ≠ 1. By comparison, continuous-time random walks lead via generalized master equations to an integro-differential picture. Using Lévy 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).