  A microscopic model able to describe simultaneously the dynamic viscosity and
the self-diffusion coefficient of fluids is presented. This model is shown to
emerge from the introduction of fractional calculus in a usual model of
condensed matter physics based on an elastic energy functional. The main
feature of the model is that all measurable quantities are predicted to depend
in a non-trivial way on external parameters (e.g. the experimental set-up
geometry, in particular the sample size). On the basis of an unprecedented
comparative analysis of a collection of published experimental data, the
modeling is applied to the case of water in all its fluid phases, in particular
in the supercooled phase. It is shown that the discrepancies in the literature
data are only apparent and can be quantitavely explained by the different
experimental configurations. This approach makes it possible to reproduce the
water viscosity with a better accuracy than the 2008 IAPWS formulation and also
with a more physically satisfying modeling of the isochors. Moreover, it also
allows the modeling within experimental accuracy of the translational
self-diffusion data available in the literature in all water fluid phases.
Finally, the formalism of the model makes it possible to understand the
anomalies observed on the dynamic viscosity and self-diffusion coefficient and
their possible links.
