Particle Spectra and Mass Composition in the Ultra-High Energy Region in the Framework of the Galactic Origin of Cosmic Rays

The possibility for a self-consistent description of all the basic features of the observed cosmic ray spectra and primary composition variations in the energy range of $10^{15}\div 10^{20}$ eV within the Galactic origin scenario is examined. We assume the existence of Galactic sources that accelerate particles up to $\sim 3\cdot 10^{18}Z$ eV and take into account a highly inhomogeneous (fractal-like) distribution of matter and magnetic fields in the Galaxy that leads to extremely large free paths of particles ("L\'{e}vy flights"), along with an overwhelming contribution to the cosmic ray fluxes observed above $\sim 10^{18}$ eV from particles reaching the Solar System without scattering. Our scenario was refined on the basis of recent experimental results on primary mass composition. Model predictions, which could be verified with the improved high-precision measurements in the nearest future are discussed.