Fractional dynamics of one-dimensional linear chain driven by power-law noise

Abstract

We investigate the fractional dynamics of $N-$Brownian particles linearly coupled by springs. Using the Caputo definition of a fractional derivative and imposing that the system is driven internally by power-law noise, we recast the generalized Langevin equation into a fractional Langevin equation. We derive the mean position of the $i^\text{th}$ particle in the linear chain using the method of Laplace transform. Our results show that for increasing exponent $\alpha$, the damping of the $i^\text{th}$ particle is increased consistent with the behavior of a fractional oscillator.