On variable-order fractional linear viscoelasticity

A generalization of fractional linear viscoelasticity based on Scarpi’s approach to variable-order fractional calculus is presented. After reviewing the general mathematical framework, a variable-order fractional Maxwell model is analysed as a prototypical example for the theory. Some physical considerations are then provided concerning the fractionalisation procedure and the choice of the transition functions. Lastly, the material functions for the considered model are derived and numerically evaluated for exponential-type and Mittag-Leffler-type order functions.