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

Bohdan Datsko, Igor Podlubny and Yuriy Povstenko
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Bohdan Datsko: Faculty of Mathematics and Applied Physics, Rzeszow University of Technology, Powstancow Warszawy 8, 35-959 Rzeszow, Poland
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

Mathematics, 2019, vol. 7, issue 5, 1-11

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.

Keywords: fractional calculus; mass absorption; diffusion-wave equation; Caputo derivative; harmonic impact; Laplace transform; Fourier transform; Mittag-Leffler function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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