|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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