Fractional Calculus Glasses

On Fractional Relaxation

R. Hilfer

in: Scaling and Disordered Systems
edited by: F. Family and M. Daoud and H. Herrmann and H.E. Stanley
World Scientific, Singapore, 251 (2002)
ISBN: 978-981-02-4838-3

submitted on
Monday, April 2, 2001

Generalized fractional relaxation equations based on generalized Riemann-Liouville derivatives are combined with a simple short time regularization and solved exactly. The solution involves generalized Mittag-Leffler functions. The associated frequency dependent susceptibilities are related to symmetrically broadened Cole-Cole susceptibilities occurring as Johari Goldstein β-relaxation in many glass formers. The generalized susceptibilities exhibit a high frequency wing and strong minimum enhancement.

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