Subordination Principle for Generalized Fractional Zener Models

The fractional Zener constitutive law is frequently used as a model of solid-like viscoelastic behavior. In this work, class linear models type, which generalize the model, studied by use Bernstein functions technique. We prove that corresponding relaxation moduli are completely monotone under appropriate thermodynamic restrictions on parameters. Based property, we study propagation function and establish subordination principle for Zener-type wave equation, provides an integral representation solution in terms related classical equation. analytical findings supported numerical examples.