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Wave equation for generalized Zener model containing complex order fractional derivatives

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Abstract

We study waves in a viscoelastic rod whose constitutive equation is of generalized Zener type that contains fractional derivatives of complex order. The restrictions following from the Second Law of Thermodynamics are derived. The initial boundary value problem for such materials is formulated and solution is presented in the form of convolution. Two specific examples are analyzed.

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Authors and Affiliations

  1. Institute of Mechanics, Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, Novi Sad, 21000, Serbia

    Teodor M. Atanacković

  2. Institute of Mathematics, Serbian Academy of Sciences and Arts, Kneza Mihaila 36, Belgrade, 11000, Serbia

    Marko Janev

  3. Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Trg D. Obradovića 4, Novi Sad, 21000, Serbia

    Sanja Konjik & Stevan Pilipović

Authors
  1. Teodor M. Atanacković
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  2. Marko Janev
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  3. Sanja Konjik
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  4. Stevan Pilipović
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Corresponding author

Correspondence to Sanja Konjik.

Additional information

Communicated by Andreas Öchsner.

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Atanacković, T.M., Janev, M., Konjik, S. et al. Wave equation for generalized Zener model containing complex order fractional derivatives. Continuum Mech. Thermodyn. 29, 569–583 (2017). https://doi.org/10.1007/s00161-016-0548-4

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  • DOI: https://doi.org/10.1007/s00161-016-0548-4

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