Wave equation in fractional Zener-type viscoelastic media involving Caputo–Fabrizio fractional derivatives
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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.
KeywordsWaves Zener model Caputo–Fabrizio derivative
This research was supported by the Serbian Academy of Sciences and Arts (TMA) and Serbian Ministry of Science Grants TR32035, III44003 (MJ) and 174024 (SP).
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