Review of Some Promising Fractional Physical Models
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 non-locality, power-law long-term memory or fractal properties by using integrations and differentiation of non-integer orders, i.e., by methods of 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 non-integer 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
Cite
@article{arxiv.1502.07681,
title = {Review of Some Promising Fractional Physical Models},
author = {Vasily E. Tarasov},
journal= {arXiv preprint arXiv:1502.07681},
year = {2015}
}
Comments
38 pages, LaTeX