Open Access Open Access  Restricted Access Subscription or Fee Access

Compatibility between Fractional Hamiltonian Formalisms

Pierre Inizan


Some recent investigations tend to show that fractional formalism can be used to describe Hamiltonian chaos. This link appears via a peculiar comportment of the time evolution variable in such systems. In this paper, we first present a modelisation of time introduced by A.A. Stanislavsky, which leads to fractional causal equations for Hamiltonian systems. Then we expose another method based on a least action principle and developed by J. Cresson, to obtain fractional Hamiltonian equations. In the general case, such equations are non causal, but we prove that some restrictions can lead to causal ones. Hence we conclude that those two formalisms are compatible ; starting with this modelisation of time, Hamiltonian systems can be described with fractional causal equations, stemming from a least action principle. Keywords: Lagrangian and Hamiltonian dynamics, fractional calculus, least action principle, subordinated process.

Full Text:


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information.