Authors: Konjik, Sanja
Oparnica, Ljubica
Zorica, Dušan 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Waves in viscoelastic media described by a linear fractional model
Journal: Integral Transforms and Special Functions
Volume: 22
Issue: 4-5
First page: 283
Last page: 291
Issue Date: 1-Apr-2011
Rank: M21
ISSN: 1065-2469
DOI: 10.1080/10652469.2010.541039
Recently, the classical wave equation has been generalized for the case of viscoelastic media described by the fractional Zener model (cf. [S. Konjik, Lj. Oparnica, and D. Zorica,Waves in fractional Zener type viscoelastic media, J. Math. Anal. Appl. (2009), doi:10.1016/j.jma.2009.10.043]). In this article, we use a more general fractional model for a viscoelastic body to describe the wave equation for viscoelastic infinite media, and prove existence and uniqueness of distributional solutions to the corresponding generalized Cauchy problem.
Keywords: Fractional derivatives | Fundamental solution | Laplace and fourier transforms
Publisher: Taylor & Francis
Project: Viscoelasticity of fractional type and shape optimization in a theory of rods 
Methods of Functional and Harmonic Analysis and PDE with Singularities 
Austrian Science Fund, START-project Y-237

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