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

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.

References in corpus (3)

• Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics
• Variational Problems with Fractional Derivatives: Euler-Lagrange Equations
• Distributional framework for solving fractional differential equations

Cited by in corpus (11)

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• Wave equation for generalized Zener model containing complex order fractional derivatives
• Energy balance for fractional anti-Zener and Zener models in terms of relaxation modulus and creep compliance
• Fractional Burgers wave equation
• Error Estimates for Approximations of Distributed Order Time Fractional Diffusion with Nonsmooth Data
• 0-Gaps on 3D Digital Curves
• Fractional Burgers wave equation on a finite domain