# Short note on the emergence of fractional kinetics

Source: [Short note on the emergence of fractional kinetics](<https://www.sota2.com/research/paper/68fa31421e209131ce87cd28>)

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

Data updated: 2025-10-24T18:43:03.821Z

Authors: Gianni Pagnini

Published: 2014-04-01T12:28:33.000Z

## Abstract

In the present Short Note an idea is proposed to explain the emergence and the observation of processes in complex media that are driven by fractional non-Markovian master equations. Particle trajectories are assumed to be solely Markovian and described by the Continuous Time Random Walk model. But, as a consequence of the complexity of the medium, each trajectory is supposed to scale in time according to a particular random timescale. The link from this framework to microscopic dynamics is discussed and the distribution of timescales is computed. In particular, when a stationary distribution is considered, the timescale distribution is uniquely determined as a function related to the fundamental solution of the space-time fractional diffusion equation. In contrast, when the non-stationary case is considered, the timescale distribution is no longer unique. Two distributions are here computed: one related to the M-Wright/Mainardi function, which is Green's function of the time-fractional diffusion equation, and another related to the Mittag-Leffler function, which is the solution of the fractional-relaxation equation.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1404.0215>)

[PDF](<https://arxiv.org/pdf/1404.0215.pdf>)