Complex fractional Zener model of wave propagation in ℝ

Abstract

Abstract The classical wave equation is generalized within fractional framework, by using fractional derivatives of real and complex order in the constitutive equation, so that it describes wave propagation in one dimensional infinite viscoelastic rod. We analyze existence, uniqueness and properties of solutions to the corresponding initial-boundary value problem for generalized wave equation. Also, we provide a comparative analysis with the case of the same equation but considered on a bounded or half-bounded spatial domain. We conclude our investigation with a numerical example that illustrates obtained results.