Some Applications of Fractional Calculus in Elementary Physics

Abstract

A brief introduction to development of fractional calculus, particularly with time as independent variable, and its importance in taking care of memory effects has been given. As expository applications of this, topics of Newton’s second law of motion and equations of motion, a body falling under gravity in a viscous medium, projectile motion in a resistive medium, simple oscillator, Fourier law of heat conduction, Newton’s law of cooling, Ohm’s law and RC, RL circuits, and physics of decay / growth / relaxation processes, have been dealt with. The objective of this article is not only to put forth the well-established things from introductory physics in different perspective but also to bring out the need to include the old (almost as much as the classical calculus) and yet offbeat topic of fractional calculus as a part of our curriculum at some stage, and, thus, prepare the next generation to capture the richness underlying the complex systems in nature.