Fractional Powers of Derivatives in Classical Mechanics

Details Fractional Powers of Derivatives in Classical Mechanics Fractional Powers of Derivatives in Classical Mechanics

2011-07-28

arxiv.org/abs/1107.5682v1

Communications in Applied Analysis 12 (2008) 441-450

Physics

Classical Physics

10 pages, LaTeX

Scientific paper

Fractional analysis is applied to describe classical dynamical systems. Fractional derivative can be defined as a fractional power of derivative. The infinitesimal generators {H, .} and L=G(q,p) \partial_q+F(q,p) \partial_p, which are used in equations of motion, are derivative operators. We consider fractional derivatives on a set of classical observables as fractional powers of derivative operators. As a result, we obtain a fractional generalization of the equation of motion. This fractional equation is exactly solved for the simple classical systems. The suggested fractional equations generalize a notion of classical systems to describe dissipative processes.

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