Magnetorheological elastomer (MRE)-based semi-active vibration mitigation device demands a mathematical representation of its smart characteristics. To model the material behavior over broadband frequency, the simplicity of the mathematical formulation is very important. Material modeling of MRE involves the theory of viscoelasticity, which describes the properties intermediate between the solid and the liquid. In the present study, viscoelastic property of MRE is modeled by an integer and fractional order derivative approaches. Integer order-based model comprises of six parameters, and the fraction order model is represented by five parameters. The parameters of the model are identified by minimizing the error between the response from the model and the dynamic compression test data. Performance of the model is evaluated with respect to the optimized parameters estimated at different sets of regularly spaced arbitrary input frequencies. A linear and quadratic interpolation function is chosen to generalize the variation of parameters with respect to the magnetic field and frequency. The predicted response from the model revealed that the fractional order model describes the properties of MRE in a simplest form with reduced number of parameters. This model has a greater control over the real and imaginary part of the complex stiffness, which facilitates in choosing a better interpolating function to improve the accuracy. Furthermore, it is confirmed that the realistic assessment on the performance of a model is based on its ability to reproduce the results obtained from optimized parameters.