# Spectra of protons and nuclei in the energy range of ${10^{10}\div10^{20}}$ eV in the framework of Galactic cosmic ray origin

## TL;DR

This paper models the Galactic cosmic ray spectrum from 10^10 to 10^20 eV using anomalous diffusion, successfully explaining key spectral features and composition variations observed locally.

## Contribution

It introduces a novel application of anomalous diffusion equations to reproduce cosmic ray spectral features across a wide energy range.

## Key findings

- Reproduces the spectral 'knee' and flattening at high energies.
- Explains the difference in spectral exponents between protons and nuclei.
- Predicts the behavior of mass composition at ultra-high energies.

## Abstract

We consider the problem of the cosmic ray spectrum formation assuming that cosmic rays are produced by Galactic sources. The anomalous diffusion equation proposed in our recent papers is used to describe cosmic ray propagation in the interstellar medium. We show that in the framework of this approach and with generation spectrum exponent $\gamma=2.85$ it is possible to reproduce locally observed basic features of cosmic rays in the energy region of $10^{10}\div 10^{20}$ eV: difference between spectral exponents of protons and other nuclei, mass composition variation, `knee' problem, flattening of the primary spectrum at $E \geq 10^{18}\div 10^{19}$ eV. The crucial model predictions for the mass composition behaviour in the ultra-high energy region are discussed.