Fractional diffusion of cosmic rays

Abstract

We consider the propagation of galactic cosmic rays under assumption that the interstellar medium is a fractal one. An anomalous diffusion equation in terms of fractional derivatives is used to describe of cosmic ray propagation. The anomaly in used model results from large free paths ("Levy flights") of particles between galactic inhomogeneities and long time a particle stays in a trap. An asymptotical solution of the anomalous diffusion equation for point instantaneous and impulse sources with inverse power spectrum relating to supernova bursts is found. It covers both subdiffusive and superdiffusive regimes and is expressed in terms of the stable distributions. The energy dependence of spectral exponent of observed particles in different regimes is discussed.