The role of Mittag-Leffler functions in anomalous relaxation

Derrick Crothers, D. Holland, Y.P. Kalmykov, W.T. Coffey

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)

Abstract

The inertia-corrected Debye model of rotational Brownian motion of polar molecules was generalized by Coffey et al. [Phys. Rev. E, 65, 32 102 (2002)] to describe fractional dynamics and anomalous rotational diffusion. The linear- response theory of the normalized complex susceptibility was given in terms of a Laplace transform and as a function of frequency. The angular-velocity correlation function was parametrized via fractal Mittag-Leffler functions. Here we apply the latter method and complex-contour integral- representation methods to determine the original time-dependent amplitude as an inverse Laplace transform using both analytical and numerical approaches, as appropriate. (C) 2004 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)27-34
Number of pages8
JournalJournal of Molecular Liquids
Volume114
Issue number1-3
Publication statusPublished - 15 Sep 2004

ASJC Scopus subject areas

  • Physical and Theoretical Chemistry
  • Atomic and Molecular Physics, and Optics

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