Average value of the cosmic ray injection exponent at Galactic sources

Abstract: The energy spectrum of high energy cosmic rays emitted by sources change during propagation in the Galaxy. Using the spectrum observed at the Earth and two different transport models, based on anomalous and normal diffusion equations, we have retrieved an average value of the cosmic ray injection exponent at Galactic sources taking into account the inhomogeneity of the interstellar medium. We have shown that the average value of the injection index $p$, obtained in the framework of both transport models, equals to $p\sim (2.8-3.0)$.