Waves propagation in a fractional viscoelastic continuum

In this paper the analysis of waves scattering in a fractional-type viscoelasticmaterial is analyzed. Such a material involves, in the constitutive equation, the presence of nonintegerorder derivatives of the strain filed yielding a memory-type behavior of the material model.The presence of such a term has been also justified experimentally reporting the relaxationmodulus of polymeric materials, obtained from experimental test, that are well-fitted by a powerlawof fractional order. Some numerical applications reporting the standing-waves condition of an1D solid varying the fractional differentiation order has also been reported in the paper.