Authors: Atanacković, Teodor
Janev, Marko 
Konjik, Sanja
Pilipović, Stevan
Title: Complex fractional Zener model of wave propagation in
Journal: Fractional Calculus and Applied Analysis
Volume: 21
Issue: 5
First page: 1313
Last page: 1334
Issue Date: 25-Oct-2018
Rank: M21a
ISSN: 1311-0454
DOI: 10.1515/fca-2018-0069
Abstract: 
The classical wave equation is generalized within fractional framework, by using fractional derivatives of real and complex order in the constitutive equation, so that it describes wave propagation in one dimensional infinite viscoelastic rod. We analyze existence, uniqueness and properties of solutions to the corresponding initial-boundary value problem for generalized wave equation. Also, we provide a comparative analysis with the case of the same equation but considered on a bounded or half-bounded spatial domain. We conclude our investigation with a numerical example that illustrates obtained results.
Keywords: constitutive equation | fractional derivative of complex order | thermodynamical restriction | wave propagation
Publisher: de Gruyter
Project: Viscoelasticity of fractional type and shape optimization in a theory of rods 
Methods of Functional and Harmonic Analysis and PDE with Singularities 
Development of Dialogue Systems for Serbian and Other South Slavic Languages 
Biosensing Technologies and Global System for Long-Term Research and Integrated Management of Ecosystems 
Provincial Secretariat for Science, Grant no. 114-451-2098

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