Response characteristics of a fractional oscillator

The integral equation of motion of a driven fractional oscillator is obtained by generalizing the corresponding equation of motion of a driven harmonic oscillator to include integrals of arbitrary order according to the methods of fractional calculus. The Green's function solution for the fractional oscillator is obtained in terms of Mittag–Leffler functions using Laplace transforms. The response and resonance characteristics of the fractional oscillator are studied for several cases of forcing function.