Solutions for a fractional diffusion equation with radial symmetry and integro-differential boundary conditions

Solutions for a fractional diffusion equation with radial symmetry and integro-differential boundary conditions

E. K. Lenzi, D. S. Vieira, M. K. Lenzi, G. G. Lenzi, D. P. Leitoles, Thermal Science 19, S1-S6 (2015).
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The solutions for a dimensional system with radial symmetry and governed by a fractional diffusion equation have been investigated. More specifically, a spherical system was considered, being defined in the semi – infinity interval [R, ¥) and subjected to surface effects described in terms of integro – differential boundary conditions which has many practical applications. The analytical solutions were obtained by using the Green function approach, showing a broad range of different behaviors which can be related to anomalous diffusion. The analyses also considered the influence of the parameters of the analytical solution in order to describe a more realistic scenario.