Abstract: We start with basic mathematical statements about some roots of the Fractional Calculus. At the same time, we will consider some basic aspects related to the conceptual convergence with the well established experimental framework of Classical and Quatum Mechanics. Finally and in the framework of Fractional Calculus, we will analyze some fudamental issues involved in the study of the atmospheric dust dynamics and the meteorological instruments associated to the landers in the Martian missions.