This article is cited in 36 papers

REVIEWS OF TOPICAL PROBLEMS

Fractional phenomenology of cosmic ray anomalous diffusion

V. V. Uchaikin

Ul'yanovsk State University

Abstract: We review the evolution of the cosmic ray diffusion concept from the ordinary (Einstein) model of Brownian motion to the fractional models that appeared in the last decade. The mathematical and physical foundations of these models are discussed, as are their consequences, related problems, and prospects for further development.

Keywords: Fractional derivatives, fractional Laplacian, fractals, turbulence, percolation, plasma, stable distributions.

PACS: 02.50.-r, 05.40.-a, 98.70.Sa

MSC: 85-02

Received: December 3, 2012
Revised: April 12, 2013
Accepted: May 16, 2013

DOI: 10.3367/UFNr.0183.201311b.1175

 English version: Physics–Uspekhi, 2013, 56:11, 1074–1119

Bibliographic databases:

• 
• 
• 
• 
•