## Journal of Physical Mathematics

### Relaxation Equations: Fractional Models

#### Abstract

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

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

Dates
First available in Project Euclid: 31 August 2017