Time-Fractional Diffusion with Mass Absorption in a Half-Line Domain due to Boundary Value of Concentration Varying Harmonically in Time

Yuriy Povstenko; Tamara Kyrylych

doi:10.3390/e20050346

Time-Fractional Diffusion with Mass Absorption in a Half-Line Domain due to Boundary Value of Concentration Varying Harmonically in Time

Entropy (Basel). 2018 May 6;20(5):346. doi: 10.3390/e20050346.

Authors

Yuriy Povstenko¹, Tamara Kyrylych²

Affiliations

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.

Abstract

The time-fractional diffusion equation with mass absorption is studied in a half-line domain under the Dirichlet boundary condition varying harmonically in time. The Caputo derivative is employed. The solution is obtained using the Laplace transform with respect to time and the sin-Fourier transform with respect to the spatial coordinate. The results of numerical calculations are illustrated graphically.

Keywords: Caputo derivative; Laplace transform; Mittag–Leffler function; fractional calculus; sin-Fourier transform.