Journal of Physical Mathematics

Relaxation Equations: Fractional Models

Rosa CFAE and Capelas de Oliveira E

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


The relaxation functions introduced empirically by Debye, Cole-Cole, Cole-Davidson and Havriliak-Negami are, each of them, solutions to their respective kinetic equations. In this work, we propose a generalization of such equations by introducing a fractional differential operator written in terms of the Riemann-Liouville fractional derivative of order $γ$, $0\ltγ\le1$. In order to solve the generalized equations, the Laplace transform methodology is introduced and the corresponding solutions are then presented, in terms of Mittag-Leffler functions. In the case in which the derivative’s order is $γ = 1$, the traditional relaxation functions are recovered. Finally, we presented some 2D graphs of these function.

Article information

J. Phys. Math., Volume 6, Number 2 (2015), 7 pages.

First available in Project Euclid: 31 August 2017

Permanent link to this document

Digital Object Identifier

Mittag-Leffler functions Laplace transform Riemann-Liouville derivative fractional differential equations dielectric relaxation complex susceptibility relaxation function response function Debye Cole-Cole Davidson-Cole Havriliak-Negami


CFAE, Rosa; E, Capelas de Oliveira. Relaxation Equations: Fractional Models. J. Phys. Math. 6 (2015), no. 2, 7 pages. doi:10.4172/2090-0902.1000146.

Export citation