Authors: Konjik, Sanja
Oparnica, Ljubica
Zorica, Dušan 
Title: Distributed-order fractional constitutive stress–strain relation in wave propagation modeling
Journal: Zeitschrift fur Angewandte Mathematik und Physik
Volume: 70
Issue: 2
Issue Date: 1-Apr-2019
Rank: M21
ISSN: 0044-2275
DOI: 10.1007/s00033-019-1097-z
Abstract: 
Distributed-order fractional model of viscoelastic body is used to describe wave propagation in an infinite media. Existence and uniqueness of fundamental solution to the generalized Cauchy problem is obtained explicitly. The wave propagation speed is found to be related to the material properties at initial time. The fundamental solutions corresponding to four thermodynamically acceptable classes of linear fractional constitutive models and power-type distributed-order models are also obtained.
Keywords: Distributed-order model of viscoelastic body | Fractional derivative | Linear fractional model | Power-type distributed-order model | Wave equation
Publisher: Springer Link
Project: Viscoelasticity of fractional type and shape optimization in a theory of rods 
Methods of Functional and Harmonic Analysis and PDE with Singularities 
Provincial Secretariat for Higher Education and Scientific Research, Grant 142-451-2489

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