Mixed convolved action for the fractional derivative Kelvin–Voigt model

Abstract

Based upon the concept of mixed convolved action, a true variational statement for a fractional derivative Kelvin–Voigt model is presented. In this formulation, a single functional is defined as a series of convolution integrals, where the stationarity of this functional leads to all the governing differential equations as well as pertinent initial conditions. Thus, the entire description of a fractional-derivative Kelvin–Voigt model is encapsulated within this framework. This new formulation provides an elegant basis for a development of effective numerical methods involving finite element representation over a temporal domain. Here, the simplest temporal finite element approach is developed, and some computational examples are provided to validate this proposed approach.