Perturbative experiments in magnetically confined fusion plasmas have shown that edge cold pulses travel to the centre of the device on a time scale much faster than expected on the basis of diffusive transport. An open issue is whether the observed fast pulse propagation is due to non-local transport mechanisms or if it could be explained on the basis of local transport models. To elucidate this distinction, perturbative experiments involving ICRH power modulation in addition to cold pulses have been conducted in JET for the same plasma. Local transport models have found problematic the reconciliation of the fast propagation of cold pulses with the comparatively slower propagation of heat waves generated by power modulation. In this paper, a non-local model based on the use of fractional diffusion operators is used to describe these experiments. A numerical study of the parameter dependence of the pulse speed and the amplitude and phase of the heat wave is also presented.