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Time-Fractional Diffusion-Wave Equation with Mass Absorption in a Sphere under Harmonic Impact

Author

Listed:
  • Bohdan Datsko

    (Faculty of Mathematics and Applied Physics, Rzeszow University of Technology, Powstancow Warszawy 8, 35-959 Rzeszow, Poland
    Institute for Applied Problems of Mechanics and Mathematics NAS of Ukraine, 79060 Lviv, Ukraine)

  • Igor Podlubny

    (BERG Faculty, Technical University of Kosice, B. Nemcovej 3, 04200 Kosice, Slovakia)

  • Yuriy Povstenko

    (Faculty of Mathematical and Natural Sciences, Jan Dlugosz University in Czestochowa, Armii Krajowej 13/15, 42-200 Czestochowa, Poland)

Abstract

The time-fractional diffusion equation with mass absorption in a sphere is considered under harmonic impact on the surface of a sphere. The Caputo time-fractional derivative is used. The Laplace transform with respect to time and the finite sin-Fourier transform with respect to the spatial coordinate are employed. A graphical representation of the obtained analytical solution for different sets of the parameters including the order of fractional derivative is given.

Suggested Citation

  • Bohdan Datsko & Igor Podlubny & Yuriy Povstenko, 2019. "Time-Fractional Diffusion-Wave Equation with Mass Absorption in a Sphere under Harmonic Impact," Mathematics, MDPI, vol. 7(5), pages 1-11, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:433-:d:231755
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    References listed on IDEAS

    as
    1. Vitali, Silvia & Castellani, Gastone & Mainardi, Francesco, 2017. "Time fractional cable equation and applications in neurophysiology," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 467-472.
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