Generalization of a theoretical basis for the application of fractional calculus to viscoelasticity

This work investigates the effect a fractional derivative may have on the spectrum of relaxation modes of a viscoelastic material. It is shown that the order of the fractional derivative results in a modification to the constitutive relationships that exist within the Rouse model for viscoelasticity. These relationships that are used in engineering analyses have been previously developed from an empirical standpoint. The resulting modification to these constitutive relationships further supports the inclusion of fractional calculus in models of viscoelastic materials and hence increase their level of confidence associated with their usage.