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Fractional Diffusion Equation with Spherical Symmetry and Reactive Boundary Conditions

Lenzi M. K., Lenzi E. K., Novatski A., Menechini N. R., da Silva L. R.

Fundamenta Informaticae

2017

Vol. 151, nr 1/4

341--354

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.