This article focuses on fractional Maxwell model of viscoelastic materials, which are a generalization of classic Maxwell model to noninteger order derivatives. We present and discuss formulations of the fractional order viscoelastic model and give physical interpretations of the model by using viscoelastic functions. We apply the generalized Caputo fractional derivative to viscoelastic models, namely fractional Maxwell model, fractional Kelvin‐Voigt model, and fractional Zener model. The stress relaxation module and creep compliance for each model are derived analytically using generalized Caputo fractional derivative. We analyze effect of α and newly introduced parameter ρ in all these models. The result shows an effect on viscoelastic models using fractional operator.