A study of sinusoidally forced oscillations of a fractional oscillator shows that the system exhibits a rich variety of damping characteristics. While some aspects of the damping mimic the characteristic features of a damped harmonic oscillator, there are others, which do not find any parallel...

It is well known that Brownian diffusion is characterized by a mean-squared displacement which varies linearly in time, 〈r2〉∼t and that anomalous diffusion, by a mean-square displacement which is nonlinear in time, 〈r2〉∼tα. It is generally accepted that fractional diffusion, which...

The integral equation of motion of a simple harmonic oscillator is generalized by taking the integral to be of arbitrary order according to the methods of fractional calculus to yield the equation of motion of a fractional oscillator. The solution is obtained in terms of Mittag–Leffler...