  We investigate some basic applications of Fractional Calculus (FC) to
Newtonian mechanics. After a brief review of FC, we consider a possible
generalization of Newton's second law of motion and apply it to the case of a
body subject to a constant force. In our second application of FC to Newtonian
gravity, we consider a generalized fractional gravitational potential and
derive the related circular orbital velocities. This analysis might be used as
a tool to model galactic rotation curves, in view of the dark matter problem.
Both applications have a pedagogical value in connecting fractional calculus to
standard mechanics and can be used as a starting point for a more advanced
treatment of fractional mechanics.
