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arXiv · 1502.07681

Review of Some Promising Fractional Physical Models

Vasily E. Tarasov
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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.

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Vasily E. Tarasov. 2015-02-14. Review of Some Promising Fractional Physical Models. https://doi.org/10.1142/s0217979213300053

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