, Volume 54, Issue 1–2, pp 155–167 | Cite as

Wave equation in fractional Zener-type viscoelastic media involving Caputo–Fabrizio fractional derivatives

  • Teodor M. AtanackovićEmail author
  • Marko Janev
  • Stevan Pilipović


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.


Waves 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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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  • Teodor M. Atanacković
    • 1
    Email author
  • Marko Janev
    • 2
  • Stevan Pilipović
    • 3
  1. 1.Serbian Academy of Arts and SciencesBelgradeSerbia
  2. 2.Institute of MathematicsSerbian Academy of Sciences and ArtsBelgradeSerbia
  3. 3.Department of Mathematics and Informatics, Faculty of SciencesUniversity of Novi SadNovi SadSerbia

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