Perturbative experiments in fusion plasmas have shown that edge cold pulses travel to the center 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 to reconcile the fast propagation of the cold pulses with the comparatively slower propagation of the 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. The proposed non-local model is able to reproduce the profiles of the amplitude and the phase of the electron temperature heat waves excited by the ICRH modulation in JET. Most importantly, for the same model parameter values, the model can successfully accommodate the propagation of pulses with time delays comparable to those in the experiment, ~4ms. We also present a numerical study of the parameter dependence of the transport properties of the fractional model, and discuss the role of non-locality in the flux-gradient dependence.