From stretched exponential to inverse power-law: Fractional dynamics, Cole-Cole relaxation processes, and beyond

Ralf Metzler, Joseph Klafter

Research output: Contribution to journalArticlepeer-review

Abstract

We present a generalisation of the classical exponential relaxation based on the fractional Fokker-Planck equation framework. We show how fractional dynamics modifies the Brownian dynamics underlying standard relaxation processes, and gives rise to the Mittag-Leffler relaxation of modes and moments. The latter is characterised through a turnover from an initial stretched exponential to a final inverse power-law pattern and the associated complex susceptibility corresponds to the Cole-Cole pattern.

Original languageEnglish
Pages (from-to)81-87
Number of pages7
JournalJournal of Non-Crystalline Solids
Volume305
Issue number1-3
DOIs
StatePublished - Jul 2002

Fingerprint

Dive into the research topics of 'From stretched exponential to inverse power-law: Fractional dynamics, Cole-Cole relaxation processes, and beyond'. Together they form a unique fingerprint.

Cite this