Authors: Atanacković, Teodor
Pilipović, Stevan
Zorica, Dušan 
Title: Distributed-order fractional wave equation on a finite domain. Stress relaxation in a rod
Journal: International Journal of Engineering Science
Volume: 49
Issue: 2
First page: 175
Last page: 190
Issue Date: 1-Feb-2011
Rank: M21
ISSN: 0020-7225
DOI: 10.1016/j.ijengsci.2010.11.004
Abstract: 
We study waves in a viscoelastic rod of finite length. Viscoelastic material is described by a constitutive equation of fractional distributed-order type with the special choice of weight functions. Prescribing boundary conditions on displacement, we obtain displacement and stress in a stress relaxation test. We use the Laplace transformation method in the time domain as a tool for solving system of differential and integro-differential equations, that describe the motion of the rod.
Keywords: Distributed-order fractional derivative | Distributed-order wave equation | Fractional derivative | Fractional viscoelastic material | Stress relaxation
Publisher: Elsevier
Project: Serbian Ministry of Science, Projects 144019 and 144016

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