Spectrum and fraction of cosmic ray positrons: results of the anomalous
  diffusion approach
  We present the results of new calculations of the energy spectra of cosmic
ray electrons, positrons and also positron fraction under assumption that both
electrons and positrons are generated by the same Galactic sources, which
accelerate particles with same power-law injection spectral index $p$. The
value of the injection index $p\approx 2.85$ retrieved in our works from the
analysis of the observed CR spectra has been used. The propagation of particles
through the highly non-homogeneous interstellar medium has been described by
the anomalous diffusion model.
  We show that proposed approach allows the self-consistent description of the
recent AMS-02 data. In contrast to the conclusion made by AMS-02 collaboration
about the different origin of the high-energy positrons and electrons, our
results demonstrate that the differing behavior of spectral indices of
electrons and positrons with energy can be described under the assumption that
both positrons and electrons have common Galactic sources.
  Our prediction (Lagutin et al. Bull. Russian Academy of Sciences. Physics,
2013, Vol. 77, No. 11, p. 1312) that the $e^{+}$ to total $e^{-} + e^{+}$ ratio
reaches a constant value for E $\gg 200$ GeV is confirmed.
