Coupled oscillators with power-law interaction and their fractional   dynamics analogues
  The one-dimensional chain of coupled oscillators with long-range power-law interaction is considered. The equation of motion in the infrared limit are mapped onto the continuum equation with the Riesz fractional derivative of order $\alpha$, when $0<\alpha<2$. The evolution of soliton-like and breather-like structures are obtained numerically and compared for both types of simulations: using the chain of oscillators and using the continuous medium equation with the fractional derivative. 
Nickolay Korabel, George M. Zaslavsky and Vasily E. Tarasov