Short note on the emergence of fractional kinetics

Gianni Pagnini

Physica A: Statistical Mechanics and its Applications, 2014, vol. 409, issue C, 29-34

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.

Keywords: Fractional kinetics; Continuous Time Random Walk; Superposition; Mittag-Leffler function; M-Wright/Mainardi function (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:409:y:2014:i:c:p:29-34

DOI: 10.1016/j.physa.2014.03.079

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