The main aim of this study is to develop prediction equations of asphalt mastic fractional model parameters based on the fractional model parameters of asphalt binder, taking into consideration many parameters including, styrene–butadienestyrene (SBS) and polyphosphoric acid (PPA) modification, modifier’s dosage, volume filling rate of siliceous filler, and test temperature. Experimental tests were conducted on original, SBS- and PPA-modified asphalt binders and asphalt mastics fabricated with these binders by using a dynamic shear rheometer device to achieve this aim. The asphalt mastic samples were fabricated considering a couple of volume filling rates of siliceous filler: 18 and 35%. Then, a fractional viscoelastic and the generalized Maxwell model were implemented and compared to describe the viscoelastic behavior of binder and mastic samples. The results showed that the fractional viscoelastic model could accurately predict the viscoelastic behavior of the original and modified asphalt mastic using fewer parameters compared to the well-known generalized Maxwell model so that the fitting accuracy of all samples is more than 0.99. In addition, the response surface methodology (RSM) was used to develop the prediction equation between the parameters of modified asphalt binders and the correspondent asphalt mastic fractional model. R2 values of SBS and PPA prediction models for fractional model coefficients are between 0.89 and 0.96. The predictive models presented a high accuracy so that mastic parameters with asphalt binder parameters, additive’s percentage, temperature, and volume filling rate can be achieved.