Application of differential operator with servo-order function in model of viscoelastic deformation process

The aim of the present paper is the application of a differential operator of variable order in constitutive relations for viscoelastic material. The dependence of the order function on the strain and strain rate is evaluated on the basis of known experimental results on deformation of polymeric materials. Established dependences are used for studying the vibrations of a 1-degree-of-freedom oscillator, in which the viscoelastic deformation is governed by a servo order function.