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Article

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

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Faculty of Mathematics and Applied Physics, Rzeszow University of Technology, Powstancow Warszawy 8, 35-959 Rzeszow, Poland
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Institute for Applied Problems of Mechanics and Mathematics NAS of Ukraine, 79060 Lviv, Ukraine
3
BERG Faculty, Technical University of Kosice, B. Nemcovej 3, 04200 Kosice, Slovakia
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Faculty of Mathematical and Natural Sciences, Jan Dlugosz University in Czestochowa, Armii Krajowej 13/15, 42-200 Czestochowa, Poland
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(5), 433; https://doi.org/10.3390/math7050433
Received: 24 April 2019 / Revised: 10 May 2019 / Accepted: 12 May 2019 / Published: 16 May 2019
(This article belongs to the Special Issue Fractional Order Systems)
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. View Full-Text
Keywords: fractional calculus; mass absorption; diffusion-wave equation; Caputo derivative; harmonic impact; Laplace transform; Fourier transform; Mittag-Leffler function fractional calculus; mass absorption; diffusion-wave equation; Caputo derivative; harmonic impact; Laplace transform; Fourier transform; Mittag-Leffler function
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MDPI and ACS Style

Datsko, B.; Podlubny, I.; Povstenko, Y. Time-Fractional Diffusion-Wave Equation with Mass Absorption in a Sphere under Harmonic Impact. Mathematics 2019, 7, 433. https://doi.org/10.3390/math7050433

AMA Style

Datsko B, Podlubny I, Povstenko Y. Time-Fractional Diffusion-Wave Equation with Mass Absorption in a Sphere under Harmonic Impact. Mathematics. 2019; 7(5):433. https://doi.org/10.3390/math7050433

Chicago/Turabian Style

Datsko, Bohdan, Igor Podlubny, and Yuriy Povstenko. 2019. "Time-Fractional Diffusion-Wave Equation with Mass Absorption in a Sphere under Harmonic Impact" Mathematics 7, no. 5: 433. https://doi.org/10.3390/math7050433

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