摘要：The periodic solution of fractional oscillation equation with periodic input is
considered in this work. The fractional derivative operator is taken as, 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.
