“…On the other hand, many physical systems exhibit anomalous transport, meaning that the mean square displacement grows nonlinearly in time, i.e., ∆x 2 ∝ t γ , with γ < 1 for subdiffusion and γ > 1 for superdiffusion [1][2][3][4]. In astrophysics and space physics there are several indications of superdiffusive transport of energetic particles, which come from the observations of nonrelativistic solar electrons [5], from the analysis of energetic particle profiles observed by spacecraft at shock crossings [6][7][8][9][10], from the analysis of electron transport at the Coma cluster of galaxies [11], from the analysis of the extended precursor of supernova remnants [12,13], and from the radio-derived energy spectra of galaxy cluster merger shocks [14,15]. Furthermore, we notice that many observations of solar energetic particles are consistent with very weak pitch-angle scattering and long (even larger than one astronomical unit) mean free paths, so that "scatter free" propagation is also stemming out from measurements.…”