# Fractional Burgers wave equation

## TL;DR

This paper develops and solves fractional Burgers wave equations for viscoelastic media, revealing how different model parameters influence wave speed and propagation characteristics.

## Contribution

It introduces two classes of thermodynamically consistent fractional Burgers models and derives their analytical solutions using integral transforms.

## Key findings

- First class exhibits infinite wave propagation speed.
- Second class exhibits finite wave propagation speed.
- Spatial profiles show unexpected features in wave behavior.

## Abstract

Thermodynamically consistent fractional Burgers constitutive models for viscoelastic media, divided into two classes according to model behavior in stress relaxation and creep tests near the initial time instant, are coupled with the equation of motion and strain forming the fractional Burgers wave equations. Cauchy problem is solved for both classes of Burgers models using integral transform method and analytical solution is obtained as a convolution of the solution kernels and initial data. The form of solution kernel is found to be dependent on model parameters, while its support properties implied infinite wave propagation speed for the first class and finite for the second class. Spatial profiles corresponding to the initial Dirac delta displacement with zero initial velocity display features which are not expected in wave propagation behavior.