Fractional Models of Cosmic Ray Acceleration in the Galaxy

TL;DR

This paper introduces fractional differential equations to model cosmic ray acceleration in the galaxy, generalizing Fermi's theory to account for fractally distributed supernova remnants, providing a new mathematical framework for astrophysical particle acceleration.

Contribution

It presents a novel fractional differential equation approach to cosmic ray acceleration, extending Fermi's model to fractal distributions of supernova remnants in the galaxy.

Findings

Fractional models effectively describe cosmic ray acceleration.

Generalization of Fermi's result to fractal distributions.

Physically justified fractional differential equations.

Abstract

Possible formulations of the problem of cosmic rays acceleration in the interstellar galactic medium are considered with the use of fractional differential equations. The applied technique has been physically justified. A Fermi result has been generalized to the case of the acceleration of particles in shock waves in the supernovae remnants fractally distributed in the Galaxy.