A physical experimental study of the fractional harmonic oscillator

This article describes a laboratory component of a course in fractional calculus for undergraduates. It incorporates theoretical, experimental, and numerical analyses of the fractional harmonic oscillator. Three independent approaches were taken to obtain solutions to the fractional harmonic oscillator excited by a step function: 1) a power series expansion of the Riemann-Liouville form, 2) a circuit using fractance devices, 3) a numerical integration using the Grünwald-Letnikov algorithm. The fractional harmonic oscillator was also subjected to steady state AC excitation. In both the transient and steady state cases, the Riemann-Liouville form proved to accurately model the system dynamics. The course demonstrated that undergraduates learned the fundamental concepts of fractional calculus quite readily.