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Entropy 2017, 19(5), 203; doi:10.3390/e19050203

Fractional Diffusion in a Solid with Mass Absorption

1
Institute of Mathematics and Computer Sciences, Faculty of Mathematical and Natural Sciences, Jan Długosz University in Czȩstochowa, al. Armii Krajowej 13/15, 42-200 Czȩstochowa, Poland
2
Institute of Law, Administration and Management, Faculty of Philology and History, Jan Długosz University in Czȩstochowa, Zbierskiego 2/4, 42-200 Czȩstochowa, Poland
3
Institute of Preschool and School Education, Faculty of Pedagogy, Jan Długosz University in Czȩstochowa, Waszyngtona 4/8, 42-200 Czȩstochowa, Poland
*
Author to whom correspondence should be addressed.
Academic Editor: Gunnar Pruessner
Received: 28 March 2017 / Revised: 24 April 2017 / Accepted: 29 April 2017 / Published: 2 May 2017
(This article belongs to the Special Issue Complex Systems, Non-Equilibrium Dynamics and Self-Organisation)
View Full-Text   |   Download PDF [396 KB, uploaded 2 May 2017]   |  

Abstract

The space-time-fractional diffusion equation with the Caputo time-fractional derivative and Riesz fractional Laplacian is considered in the case of axial symmetry. Mass absorption (mass release) is described by a source term proportional to concentration. The integral transform technique is used. Different particular cases of the solution are studied. The numerical results are illustrated graphically. View Full-Text
Keywords: fractional calculus; Caputo derivative; Riesz derivative; Mittag-Leffler function; Laplace transform fractional calculus; Caputo derivative; Riesz derivative; Mittag-Leffler function; Laplace transform
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Povstenko, Y.; Kyrylych, T.; Rygał, G. Fractional Diffusion in a Solid with Mass Absorption. Entropy 2017, 19, 203.

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