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Advances in Mathematical Physics
Volume 2017 (2017), Article ID 6361598, 7 pages
Research Article

Anomalous Diffusion with an Irreversible Linear Reaction and Sorption-Desorption Process

1Departamento de Fisica, Universidade Estadual de Ponta Grossa, Avenida General Carlos Cavalcanti 4748, Ponta Grossa, PR, Brazil
2Departamento de Engenharia Qumica, Universidade Federal do Paraná, Av. Cel. Francisco H. dos Santos, 210 Jardim das Americas, 81531-990 Curitiba, PR, Brazil

Correspondence should be addressed to Ervin K. Lenzi

Received 8 May 2017; Accepted 21 June 2017; Published 25 July 2017

Academic Editor: Alkesh Punjabi

Copyright © 2017 Maike A. F. dos Santos et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We investigate the diffusion of two different species in a semi-infinite medium considering the presence of linear reaction terms. The dynamics for these species is governed by fractional diffusion equations. We also consider the presence of an adsorption-desorption boundary condition. The solutions for this system are found in terms of the function of Fox and by analyzing the behavior of the mean square displacement a rich class of diffusion processes is verified. In this sense, we show how the surface effects modify the bulk dynamics and promote an anomalous diffusion of system.