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Mathematical Problems in Engineering
Volume 2014, Article ID 107535, 7 pages
http://dx.doi.org/10.1155/2014/107535
Research Article

Extension of Matched Asymptotic Method to Fractional Boundary Layers Problems

1Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa
2Department of Mathematical Sciences, University of South Africa, Florida Sciences Campus, Florida 0003, South Africa

Received 16 June 2014; Revised 24 July 2014; Accepted 24 July 2014; Published 20 November 2014

Academic Editor: Hossein Jafari

Copyright © 2014 Abdon Atangana and Emile Franc Doungmo Goufo. 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 were concerned with the description of the boundary layers problems within the scope of fractional calculus. However, we will note that one of the main methods used to solve these problems is the matched asymptotic method. We should mention that this was not achievable via the existing fractional derivative definitions, because they do not obey the chain rule. In order to accommodate the matched asymptotic method to the scope of fractional derivative, we proposed a relatively new derivative called the beta-derivative. We presented some useful information for this operator. With the reward of this operator, we presented the idea of matched asymptotic method in finding solutions of the fractional boundary layers problems. The method was illustrated with an example.