Restrictions on parameters in distributed order fractional linear constitutive equations

We analyze a viscoelastic body in a linear stress state with the distributed order fractional derivative in the constitutive equation. The model was formulated so that it takes into account all derivatives of stress and strain between zero and one. Using a new procedure, we derive restrictions on a model that follow from the Clausius-Duhem inequality under isothermal conditions. Several constitutive equations are derived as special cases of proposed models. We apply our analysis to a creep test, a dynamical creep test and an oscillatory system.