This paper shows that mechanical models of the materials used in loudspeaker suspensions may be more accurate by incorporating fractional derivatives in the model. In conventional differential equations, the differentiating order is a real integer, whereas for fractional derivatives the order is only constrained to be a real number with a fractional piece. The results of four loudspeakers with different types of suspension show that the proposed model with a single fractional element provides very low RMS error when compared to the measured data for all loudspeakers measured in standard atmosphere as well as in vacuum. Many materials used in loudspeaker suspensions exhibit significant frequency dependence of damping and compliance due to their various viscoelastic properties. Many physical processes, including the viscoelastic materials, exhibit fractional order behavior. In addition there exists a physical interpretation of the fractional derivatives, which makes them more compelling that a purely empirical model.
https://www.aes.org/e-lib/browse.cfm?elib=18103
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