Authors: Atanacković, Teodor
Janev, Marko 
Pilipović, Stevan
Title: Wave equation in fractional Zener-type viscoelastic media involving Caputo–Fabrizio fractional derivatives
Journal: Meccanica
Volume: 54
Issue: 1-2
First page: 155
Last page: 167
Issue Date: 1-Jan-2019
Rank: M22
ISSN: 0025-6455
DOI: 10.1007/s11012-018-0920-5
Abstract: 
We investigate propagation of waves in the Zener-type viscoelastic media through a model which involves fractional derivatives with a regular kernel. The restrictions on the coefficients in the constitutive equation that follow from the weak form of the dissipation principle are obtained. We formulate a problem of motion of a spatially one dimensional continuum in a dimensionless form. Then, it is considered in the frame of distribution theory. The existence and the uniqueness of a distributional solution as well as the analysis of its regularity are presented. Numerical results provide the illustration of our approach.
Keywords: Caputo–Fabrizio derivative | Waves | Zener model
Publisher: Springer Link
Project: Integrated system for detection and estimation of fire development by real-time monitoring of critical parameters 
Methods of Functional and Harmonic Analysis and PDE with Singularities 
Development of Dialogue Systems for Serbian and Other South Slavic Languages 

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