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On a Generalized Wave Equation with Fractional Dissipation in Non-Local Elasticity

Author

Listed:
  • Teodor M. Atanackovic

    (Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovica 5, 21000 Novi Sad, Serbia)

  • Diana Dolicanin Djekic

    (Faculty of Technical Sciences, University of Pristina, Knjaza Milosa 7, 38220 Mitrovica, Serbia)

  • Ersin Gilic

    (Department of Sciences and Mathematics, State University of Novi Pazar, Vuka Karadzica 9, 36300 Novi Pazar, Serbia)

  • Enes Kacapor

    (Department of Sciences and Mathematics, State University of Novi Pazar, Vuka Karadzica 9, 36300 Novi Pazar, Serbia)

Abstract

We analyze wave equation for spatially one-dimensional continuum with constitutive equation of non-local type. The deformation is described by a specially selected strain measure with general fractional derivative of the Riesz type. The form of constitutive equation is assumed to be in strain-driven type, often used in nano-mechanics. The resulting equations are solved in the space of tempered distributions by using the Fourier and Laplace transforms. The properties of the solution are examined and compared with the classical case.

Suggested Citation

  • Teodor M. Atanackovic & Diana Dolicanin Djekic & Ersin Gilic & Enes Kacapor, 2023. "On a Generalized Wave Equation with Fractional Dissipation in Non-Local Elasticity," Mathematics, MDPI, vol. 11(18), pages 1-13, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3850-:d:1236015
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    References listed on IDEAS

    as
    1. I. Area & J. Losada & J. J. Nieto, 2014. "On Fractional Derivatives and Primitives of Periodic Functions," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, August.
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