The intrinsic damping of the fractional oscillator

We obtain analytical expressions for the time rate of change of the potential energy, the kinetic energy and the total energy of a fractional oscillator in terms of the products of Mittag–Leffler functions. We propose a definition for the intrinsic damping force of this oscillator. We obtain a general expression for this damping force. An expression for this damping force in the asymptotic limit (ωt→0) is also obtained.