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.

中文翻译：

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关于变阶分数线性粘弹性

提出了基于 Scarpi 变阶分数微积分方法的分数线性粘弹性的推广。在回顾了一般数学框架之后，分析了变阶分数麦克斯韦模型作为该理论的典型示例。然后提供了一些关于分割过程和转换函数选择的物理考虑。最后，导出所考虑模型的材料函数，并针对指数型和 Mittag-Leffler 型阶函数进行数值评估。