Fractional Diffusion Equation with Spherical Symmetry and Reactive Boundary Conditions

Issue title: Theory and Applications of Fractional Fourier Transform and its Variants

Guest editors: Yudong Zhang, Xiao-Jun Yang, Carlo Cattani, Zhengchao Dong, Ti-Fei Yuan and Liang-Xiu Han

Article type: Research Article

Authors: Lenzi, M. K.^{a; *} | Lenzi, E. K.^b | Novatski, A.^b | Menechini Neto, R.^b | da Silva, L. R.^c

Affiliations: [a] Departamento de Engenharia Química, Universidade Federal do Paraná - Curitiba, PR 81531 - 990, Brazil. lenzi@ufpr.br | [b] Departamento de Física, Universidade Estadual de Ponta Grossa - Ponta Grossa, PR 84030-900, Brazil | [c] Departamento de Físisca, Universidade Federal do Rio Grande do Norte - Natal, RN 59072-970, Brazil

Correspondence: [*] Address for correspondence: Departamento de Engenharia Química, Universidade Federal do Paraná - Curitiba, PR 81531 - 990, Brazil

Abstract: We analyze the behavior of a system governed by a fractional diffusion equation with spherical symmetry and subjected to integro–differential boundary conditions which can simulate sorption, desorption and reaction processes. We consider the processes defined in terms of kinetic equations that couple the surface processes with the bulk dynamic enable us to describe scenarios where the surface modifies the bulk dynamics and this may change the behavior on surface. This problem is presented in terms of a general formulation satisfying the mass balance and a particular application characterized by a reversible process on the surface is analyzed. For this application, we obtain exact solutions in terms of the Green function approach and evaluate the concentrations on the spherical surface and in the bulk for different processes. These results lead to a rich class of scenarios which can be related to an anomalous diffusion.

Keywords: Fractional Time Derivative, Memory Effect, Kinetic Equation, Sorption

DOI: 10.3233/FI-2017-1496

Journal: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 341-354, 2017