To promote the secondary utilization of solid waste in asphalt pavement and reduce resource waste and environmental damage, the fine solid waste powder from the secondary treatment of solid waste was used as a substitute filler to prepare asphalt mixtures. To more precisely characterize the effects of filler type and substitution ratio on the dynamic viscoelastic mechanical characteristics of asphalt mixtures, the dynamic modulus test was conducted on asphalt mixtures, while the dynamic modulus master curve of asphalt mixtures was established based on the time-temperature equivalent principle and the Sigmoidal function. The improved generalized Sigmoidal (IGS) model, five-parameter fractional Zener (FFZ) model, six-parameter fractional Zener (SFZ) model and ten-parameter fractional Zener (TFZ) model were used to construct the shrinkage frequency curves of different asphalt mixtures under different constitutive relationships, whereas the applicability of the constitutive models was further evaluated by the principal component analysis (PCA) model. The research results showed that the dynamic modulus and phase angle of the mixture exhibited a similar change rule with the variation of temperature and frequency, and the use of solid waste-based fillers could effectively reduce the effect of frequency variation on the viscoelasticity of the mixture. The dynamic modulus master curve constructed by Sigmoidal function could accurately describe the functional relationship between the dynamic modulus with loading frequency and temperature, and the variation trend of dynamic modulus in a wider frequency range was flattened with the increase in frequency, and this change rule was not affected by the substitution ratio of the filler, while the use of solid waste-based filler could reduce the dependence of the mixture on the temperature. Compared to several fractional constitutive models, the IGS model exhibited a higher fitting accuracy for the dynamic viscoelasticity of several mixtures, and with the use of solid waste-based fillers, the deviation of fitting curves gradually decreased. A comparative study showed that the fractional constitutive model was difficult to accurately describe the dynamic viscoelasticity of the mixture, and the IGS model was preferred to be recommended as a calculation model to investigate the constitutive relationship on the dynamic viscoelasticity of the mixture.