Waves in fractional Zener type viscoelastic media

TL;DR

This paper generalizes the classical wave equation to model wave propagation in viscoelastic media described by the fractional Zener model, establishing existence, uniqueness, and explicit solutions for the associated Cauchy problem.

Contribution

It introduces a fractional Zener-based wave equation and provides rigorous mathematical analysis including fundamental solution derivation.

Findings

Existence and uniqueness of the fundamental solution are proven.

Explicit solutions to the fractional wave equation are calculated.

The model extends classical wave theory to viscoelastic materials with fractional behavior.

Abstract

Classical wave equation is generalized for the case of viscoelastic materials obeying fractional Zener model instead of Hooke's law. Cauchy problem for such an equation is studied: existence and uniqueness of the fundamental solution is proven and solution is calculated.