  In the present work, we propose a new parameterization for the concentration
flux using fractional derivatives. The fractional order differential equation
in the longitudinal and vertical directions is used to obtain the concentration
distribution of contaminants in the Planetary Boundary Layer. We solve this
model and we compare the solution against both real experiments and traditional
integer order derivative models. We show that our fractional model gives very
good results in fitting the experimental data, and perform far better than the
traditional Gaussian model. In fact, the fractional model, with constant wind
speed and a constant eddy diffusivity, performs even better than some models
found in the literature where it is considered that the wind speed and eddy
diffusivity are functions of the position. The results obtained show that the
structure of the fractional order differential equation is more appropriate to
calculate the distribution of dispersed contaminants in a turbulent flow than
an integer-order differential equation. Furthermore, a very important result we
found it is that there should be a relation between the order $\alpha$ of the
fractional derivative with the physical structure of the turbulent flow.
