A note on a modified fractional Maxwell model

Abstract

In this paper we consider a modified fractional Maxwell model based on the application of Hadamard-type fractional derivatives. The model is physically motivated by the fact that we can take into account at the same time memory effects and the time-dependence of the viscosity coefficient. We obtain an ultra-slow relaxation response whose explicit analytic form is given by the Mittag-Leffler function with a logarithmic argument. We show graphically the main properties of this relaxation response, also with the asymptotic behaviour.

10 pages, 3 figures

References in corpus (2)

• A Caputo fractional derivative of a function with respect to another function
• On the application of Mittag-Leffler functions to hyperbolic-type decay of luminescence