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has been cited by the following article:

• TITLE: Nonlocal Models of Cosmic Ray Transport in the Galaxy

  AUTHORS: Vladimir V. Uchaikin

  KEYWORDS: Nonlocal Model, Anomalous Diffusion, Fractional Derivative, Fractal, Turbulence, Plasma, Cosmic Rays

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.3 No.2, January 30, 2015

  ABSTRACT: Studying the cosmic ray transport in the Galaxy, we deal with two interacting substances: charged particles and interstellar magnetic field. Two coupled local equations describe this complicated system, but elimination of one of them (say, the magnetic field equation) transforms remaining one (the cosmic rays equation) into the nonlocal form. The most popular nonlocal operators in the cosmic ray physics are integro-differential operators of fractional order. This report contains review of recent works in this direction, including original results of the author. In the last section, some specific problems are discussed: fractional operators with soft truncation of their kernels, nonlocal properties of fractional Laplacian, and a true form of the fractional material derivative.