Fractional calculus approach to dynamic problems of viscoelastic materials

This article presents a review on the application of the fractional calculus to viscoelasticity. There are several methods to treat viscoelasticity of viscoelastic materials. One such method is to use the fractional derivative model for describing the constitutive relation of the materials. The application of the fractional operator in this field, the Riemann-Liouville's fractional operator is emphasized among several definitions of the fractional operator. The survey suggests that the viscoelastic constitutive models incorporating with the fractional calculus have been well established for fairly wide range of viscoelastic materials and the advantages of adopting the fractional calculus in viscoelasticity are that the constitutive relation of some viscoelastic materials can be described accurately by the fractional calculus model with a few experimental parameters, and that the fractional calculus approach can lead to well-posed problems even when incorporated into the finite element formulation.