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Mathematical Problems in Engineering
Volume 2014, Article ID 201796, 8 pages
Research Article

On the Agaciro Equation via the Scope of Green Function

1Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa
2School of Computational and Applied Mathematics, University of Witwatersrand, Private Bag 3, Wits, Johannesburg 2050, South Africa

Received 18 October 2013; Accepted 20 November 2013; Published 21 January 2014

Academic Editor: Muhammet Kurulay

Copyright © 2014 Abdon Atangana and Innocent Rusagara. 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.


We have undertaken an investigation of a kind of third-order equation called Agaciro equation within the folder of both integer and fractional order derivative. In the way of deriving the general exact solution of this equation, we employed the philosophy of the Green function together with some integral transform operators and special functions including but not limited to the Laplace, Fourier, and Mellin transform. We presented some examples of exact solution of this class of third-order equations for integer and fractional order derivative. It is important to point out that the value of Agaciro equation can be extended to describe assorted phenomenon in sciences.