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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