The differential energy spectrum of cosmic rays from Cherenkov radiation measurements in EAS in the energy range of 1015 - 1020 eV has been compared with an anomalous diffusion model for the particles in interstellar space having fractal properties (Lagutin et al., 2001). Calculations of the spectrum have been carried out for each of five types of primary nuclei: p, He, C, Mg, Fe, and the normalization in intensity for the energy region E0~1016 eV. The close association between experimental data and calculated "all particle" spectra in form at E0 ~(1015 - 10**18) eV is found. In this case, the average mass composition of cosmic rays calculated by five components does not contradict the average mass composition from experimental data which was obtained by several of EAS characteristics in that energy region.