Dynamics of coupled fractional oscillators in a ring

Abstract

Two methods of solution were used to obtain analytical expressions for the the time fractional dynamics corresponding to i) a system consisting of N identical masses connected by Hookean springs and forming a ring, and ii) a system consisting of one impurity mass and N – 1 identical masses connected by Hookean springs for time-fractional order 1 < α ≤ 2. Solutions in terms of generalized Mittag-Leffler functions were obtained using Laplace transform and matrix methods.