  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.
