Anomalous diffusion of the cosmic rays in the fractal Galaxy

Abstract

We consider the problem of the cosmic ray spectrum formation assuming that cosmic rays are produced by galactic sources. The fractional diffusion equation proposed in our recent papers is used to describe the cosmic rays propagation in interstellar medium. We show that in the framework of this approach it is possible to explain the locally observed basic feature of the cosmic rays in the energy region 10¹⁰ ÷10²⁰ eV: distinction in spectral exponent of protons and other nuclei, mass composition variation, “knee” problem, flattering of the primary spectrum at E≥10¹⁸ ÷10¹⁹ eV.