GENERALIZED VISCOELASTIC MODELS - THEIR FRACTIONAL EQUATIONS WITH SOLUTIONS

Recently fractional calculus (FC) has encountered much success in the description of complex dynamics. In particular Fe has proved to be a v aluable tool to handle viscoelastic aspects. In this paper we construc t fractional theological constitutive equations on the basis of well k nown mechanical models, especially the Maxwell, the Kelvin-Voigt, the Zener and the Poynting-Thomson model. To this end we introduce a fract ional element, in addition to the standard purely elastic and purely v iscous elements. As we proceed to show, many of the fractional differe ntial equations which we obtain by this construction method admit clos ed form, analytical solutions in terms of Fox X-functions of the Mitta g-Leffler type.