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Compatibility between Fractional Hamiltonian Formalisms

Pierre Inizan

Abstract


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.

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