Distributed-order fractional wave equation on a finite domain. Stress relaxation in a rod

TL;DR

This paper investigates wave propagation in a finite rod with a distributed-order fractional viscoelastic model, focusing on stress relaxation using Laplace transforms to solve the resulting differential equations.

Contribution

It introduces a novel approach to modeling stress relaxation in a finite rod using distributed-order fractional derivatives with specific weight functions.

Findings

Derived solutions for stress relaxation in the rod.

Applied Laplace transform to solve complex integro-differential equations.

Provided insights into wave behavior in viscoelastic materials with fractional models.

Abstract

We study waves in a rod of finite length with a viscoelastic constitutive equation of fractional distributed-order type for the special choice of weight functions. Prescribing boundary conditions on displacement, we obtain case corresponding to stress relaxation. In solving system of differential and integro-differential equations we use the Laplace transformation in the time domain.