Nonlocal (fractional-differential) model of cosmic ray transport in the interstellar medium

Mathematical modeling of the propagation of charged particles in the interstellar medium is a key aspect of the physics of cosmic rays. Improvements in measuring systems and enhancement of statistics via the results of extraterrestrial astronomy stimulate regular revisions of the computational models. Most of the currently used approaches are based on the local model of normal diffusion, which is attracting growing criticism. Reservations about this model arise because, first, it is in conflict with the relativistic principle of maximum speed and, second, it ignores specific spatial correlations in the properties of the turbulent interstellar medium. In this regard, in a previous review article by the first author (Physics–Uspekhi 56 1074 (2013)), some arguments were adduced in favor of a nonlocal model of cosmic ray transport based on fractional differential operators. In this review, we continue expounding on the physical and mathematical properties of the fractional differential theory, with more attention focused on the procedure for incorporating the features of the interstellar medium into nonlocal operators. New results obtained in the framework of this approach are presented, compared, and discussed.