Fractional relaxation processes and fractional rheological models for the description of a class of viscoelastic materials

Following the modelling of Zener, we establish a connection between the fractional Fokker-Planck equation and the anomalous relaxation dynamics of a class of viscoelastic materials which exhibit scale-free memory. On the basis of fractional relaxation, generalisations of the classical rheological model analogues are introduced, and applications to stress–strain relaxation in filled and unfilled polymeric materials are discussed. A possible generalisation of Reinerʹs Deborah number is proposed for systems which exhibit a diverging characteristic relaxation time.