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BioMed Research International
Volume 2014, Article ID 478028, 10 pages
http://dx.doi.org/10.1155/2014/478028
Research Article

Modelling the Formation of Liver Zones within the Scope of Fractional Order Derivative

1Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9301, South Africa
2MaSIM Focus Area, North-West University, Mafikeng 2735, South Africa

Received 11 June 2014; Accepted 24 June 2014; Published 8 September 2014

Academic Editor: Carlo Cattani

Copyright © 2014 Abdon Atangana and Suares Clovis Oukouomi Noutchie. 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.

Abstract

We develop and extend earlier results related to mathematical modelling of the liver formation zone by the adoption of noninteger order derivative. The hidden uncertainties in the model are captured and controlled thanks to the Caputo derivative. The stationary states are investigated and the time-dependent solution is approximated using two recent iteration methods. In particular, we discuss the convergence of these methods by constructing a suitable Hilbert space.