The role of Mittag–Leffler functions in anomalous relaxation

Abstract

The intertia-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.