Author(s)

Gabriele U. Varieschi

Department of Physics, Loyola Marymount University, Los Angeles, CA, USA.

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.

Fractional Calculus, Fractional Differential Equations, Fractional Mechanics

Varieschi, G. (2018) Applications of Fractional Calculus to Newtonian Mechanics. Journal of Applied Mathematics and Physics, 6, 1247-1257. doi: 10.4236/jamp.2018.66105.