Wave equation for generalized Zener model containing complex order fractional derivatives

Abstract

© 2017, Springer-Verlag Berlin Heidelberg. We study waves in a viscoelastic rod whose constitutive equation is of generalized Zener type that contains fractional derivatives of complex order. The restrictions following from the Second Law of Thermodynamics are derived. The initial boundary value problem for such materials is formulated and solution is presented in the form of convolution. Two specific examples are analyzed.