Authors: Atanacković, Teodor
Janev, Marko 
Oparnica, Ljubica
Pilipović, Stevan
Zorica, Dušan 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Space-time fractional Zener wave equation
Journal: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume: 471
Issue: 2174
Issue Date: 8-Feb-2015
Rank: M21
ISSN: 1364-5021
DOI: 10.1098/rspa.2014.0614
The space-time fractional Zener wave equation, describing viscoelastic materials obeying the timefractional Zener model and the space-fractional strain measure, is derived and analysed. This model includes waves with finite speed, as well as nonpropagating disturbances. The existence and the uniqueness of the solution to the generalized Cauchy problem are proved. Special cases are investigated and numerical examples are presented.
Keywords: Cauchy problem | Fractional strain measure | Fractional Zener model | Generalized solution | Laplace and fourier transforms
Publisher: Royal Society of London
Project: Viscoelasticity of fractional type and shape optimization in a theory of rods 
Methods of Functional and Harmonic Analysis and PDE with Singularities 
Integrated system for detection and estimation of fire development by real-time monitoring of critical parameters 
Development of Dialogue Systems for Serbian and Other South Slavic Languages 
Secretariat for Science of Vojvodina, Grant 114-451-1084

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