JAMP  Vol.6 No.6 , June 2018
Applications of Fractional Calculus to Newtonian Mechanics
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.
Cite this paper: 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.

[1]   Oldham, K.B. and Spanier, J. (1974) The Fractional Calculus. Academic Press, New York-London.

[2]   Miller, K.S. and Ross, B. (1993) An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley-Interscience Publication. John Wiley & Sons, Inc., New York.

[3]   Podlubny, I. (1999) Fractional Differential Equations, Volume 198 of Mathematics in Science and Engineering. Academic Press, Inc., San Diego, CA.

[4]   Herrmann, R. (2014) Fractional Calculus: An Introduction for Physicists. World Scientific Publishing Co., Inc., River Edge, NJ.

[5]   Hilfer, R., Ed. (2000) Applications of Fractional Calculus in Physics. World Scientific Publishing Co., Inc., River Edge, NJ.

[6]   Milgrom, M. (1983) A Modification of the Newtonian Dynamics as a Possible Alternative to the Hidden Mass Hypothesis. The Astrophysical Journal, 270, 365-370.

[7]   Milgrom, M. (2001) MOND: A Pedagogical Review. Acta Physica Polonica B, 32, 3613.

[8]   Tatom, F.B. (1995) The Relationship between Fractional Calculus and Fractals. Fractals, 3, 217-229.

[9]   Nottale, L. (2010) Scale Relativity and Fractal Space-Time: Theory and Applications. Foundations of Science, 15, 101-152.

[10]   Nottale, L. (2011) Scale Relativity and Fractal Space-Time. World Scientific Publishing Company, Singapore.

[11]   Calcagni, G. (2017) Multiscale Spacetimes from First Principles. Physical Review D, 95, Article ID: 064057.

[12]   Calcagni, G. (2017) Multifractional Theories: An Unconventional Review. Journal of High Energy Physics, 2017, 138.