  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.
