TITLE:
Applications of Fractional Calculus to Newtonian Mechanics
AUTHORS:
Gabriele U. Varieschi
KEYWORDS:
Fractional Calculus, Fractional Differential Equations, Fractional Mechanics
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.6,
June
21,
2018
ABSTRACT: 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.