# Hamiltonian formulation of fractional kinetics

Source: [Hamiltonian formulation of fractional kinetics](<https://www.sota2.com/research/paper/68fa38811e209131ce8bb06d>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T22:59:36.056Z

Authors: Sumiyoshi Abe

Published: 2017-11-15T12:43:16.000Z

## Abstract

Fractional kinetic theory plays a vital role in describing anomalous diffusion in terms of complex dynamics generating semi-Markovian processes. Recently, the variational principle and associated Levy Ansatz have been proposed in order to obtain an analytic solution of the fractional Fokker-Planck equation. Here, based on the action integral introduced in the variational principle, the Hamiltonian formulation is developed for the fractional Fokker-Planck equation. It is shown by the use of Dirac's generalized canonical formalism how the equation can be recast in the Liouville-like form. A specific problem arising from temporal nonlocality of fractional kinetics is nonuniqueness of the Hamiltonian: it has two different forms. The non-equal-time Dirac-bracket relations are set up , and then it is proven that both of the Hamiltonians generate the identical time evolution.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1711.09697>)

[PDF](<https://arxiv.org/pdf/1711.09697.pdf>)