  In the present work, we propose an advection-diffusion equation with
Hausdorff deformed derivatives to stud the turbulent diffusion of contaminants
in the atmosphere. We compare the performance of our model to fit experimental
data against models with classical and Caputo fractional derivatives. We found
that the Hausdorff equation gives better results than the tradition
advection-diffusion equation when fitting experimental data. Most importantly,
we show that our model and the Caputo fractional derivative model display a
very similar performance for all experiments. This last result indicates that
regardless of the kind of non-classical derivative we use, an
advection-diffusion equation with non-classical derivative displaying power-law
mean square displacement is more adequate to describe the diffusion of
contaminants in the atmosphere than a model with classical derivatives.
Furthermore, since Hausdorff derivatives can be related to several deformed
operators, and since differential equations with the Hausdorff derivatives are
easier to solve than equations with Caputo and other non-local fractional
derivatives, our result highlights the potential of deformed derivative models
to describe the diffusion of contaminants in the atmosphere.
