Review PaperNo Access

REVIEW OF SOME PROMISING FRACTIONAL PHYSICAL MODELS

VASILY E. TARASOV

Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991, Russia

https://doi.org/10.1142/S0217979213300053Cited by:138 (Source: Crossref)

Abstract

Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law nonlocality, power-law long-term memory or fractal properties by using integrations and differentiation of non-integer orders, i.e., by methods in the fractional calculus. This paper is a review of physical models that look very promising for future development of fractional dynamics. We suggest a short introduction to fractional calculus as a theory of integration and differentiation of noninteger order. Some applications of integro-differentiations of fractional orders in physics are discussed. Models of discrete systems with memory, lattice with long-range inter-particle interaction, dynamics of fractal media are presented. Quantum analogs of fractional derivatives and model of open nano-system systems with memory are also discussed.

Keywords:

PACS: 45.10.Hj, 45.05.+x, 03.65.Yz

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