5. Conclusions

In this chapter, we have presented a brief introduction to the world of viscoelastic models capable of describing the rheology of complex fluids, and we have summarized some of the well-known classical differential and integral models.

With incorporation of ideas from fractional calculus, most of these models can be further improved, either by changing classical local operators for improved (non-local) fractional versions, or, either using new analytic functions that arise in the realm of fractional differential equations, such as the Mittag-Leffler function.

As an example, we present the fractional K-BKZ model and the recently proposed generalized PTT model. The fractional K-BKZ model allows a better description of fluid flow behavior (when compared to the generalized PTT model), but, increases the need for high computational power. Therefore, the novelty of the present work is our detailed study on the influence of the Mittag-Leffler function in shear and elongational flows of a generalized PTT model.
