Wave equation for generalized Zener model containing complex order fractional derivatives

TL;DR

This paper investigates wave propagation in a viscoelastic rod modeled with a generalized Zener constitutive equation involving complex order fractional derivatives, deriving thermodynamic restrictions and providing explicit solutions.

Contribution

It introduces a generalized Zener model with complex order fractional derivatives, formulates the initial-boundary value problem, and analyzes specific examples.

Findings

Derived thermodynamic restrictions for the model

Presented solutions in convolution form

Analyzed two specific examples

Abstract

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.