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 is reviewed. The mathematical and physical foundations of these models are discussed, as are their consequences, associated problems and prospects for further development.

PACS: 02.50.−r, 05.40.−a, 98.70.Sa (all) DOI: 10.3367/UFNe.0183.201311b.1175 URL: https://ufn.ru/en/articles/2013/11/b/ 000331111800002 2-s2.0-84893828285 2013PhyU...56.1074U Citation: Uchaikin V V "Fractional phenomenology of cosmic ray anomalous diffusion" Phys. Usp. 56 1074–1119 (2013) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Received: 3rd, December 2012, revised: 12th, April 2013, accepted: 16th, May 2013 Оригинал: Учайкин В В «Дробно-дифференциальная феноменология аномальной диффузии космических лучей» УФН 183 1175–1223 (2013); DOI: 10.3367/UFNr.0183.201311b.1175