# Variational principle for fractional kinetics and the L\\'evy Ansatz

Source: [Variational principle for fractional kinetics and the L\\'evy Ansatz](<https://www.sota2.com/research/paper/68fa30e41e209131ce87986a>)

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

Data updated: 2025-10-24T18:30:31.568Z

Authors: Sumiyoshi Abe

Published: 2013-06-09T15:04:51.000Z

## Abstract

A variational principle is developed for fractional kinetics based on the auxiliary-field formalism. It is applied to the Fokker-Planck equation with spatio-temporal fractionality, and a variational solution is obtained with the help of the L\\'evy Ansatz. It is shown how the whole range from subdiffusion to superdiffusion is realized by the variational solution, as a competing effect between the long waiting time and the long jump. The motion of the center of the probability distribution is also analyzed in the case of a periodic drift.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1306.2026>)

[PDF](<https://arxiv.org/pdf/1306.2026.pdf>)