FRACTIONAL POWERS OF DERIVATIVES IN CLASSICAL MECHANICS

TitleFRACTIONAL POWERS OF DERIVATIVES IN CLASSICAL MECHANICS
Publication TypeJournal Article
Year of Publication2008
AuthorsTARASOV, VASILYE
Volume12
Issue4
Start Page441
Pagination10
Date Published2008
ISSN1083-2564
Abstract

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 ${ L= G(q, p)∂_q + F(q, p)∂_p }$, 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.

URLhttp://www.acadsol.eu/en/articles/12/4/7.pdf
Refereed DesignationRefereed
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