We review the application of differential operators of noninteger order tothe modeling of dynamic systems. We compare all the definitions of Variable Order(VO) operators recently proposed in literature and select the VO operator that hasthe desirable property of continuous transition between integer and non-integer orderderivatives. We use the selected VO operator to connect the meaning of functional orderto the dynamic properties of a viscoelastic oscillator. We conclude that the order ofdifferentiation of a single VO operator that represents the dynamics of a viscoelasticoscillator in stationary motion is a normalized phase shift. The normalization constantis found by taking the difference between the order of the inertial term (2) and the orderof the spring term (0) and dividing this difference by the angular phase shift betweenacceleration and position in radians (π), so that the normalization constant is simply2/π.
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