The Periodic Solution of Fractional Oscillation Equation with Periodic Input - Jun-Sheng Duan (Advances in Mathematical Physics)
The periodic solution of fractional oscillation equation with periodic input is considered in this work. The fractional derivative operator is taken as  -∞Dtα, where the initial time is -∞; hence, initial conditions are not needed in the model of the present fractional oscillation equation. With the input of the harmonic oscillation, the solution is derived to be a periodic function of time t with the same circular frequency as the input, and the frequency of the solution is not affected by the system frequency c as is affected in the integer-order case. These results are similar to the case of a damped oscillation with a periodic input in the integer-order case. Properties of the periodic solution are discussed, and the fractional resonance frequency is introduced.