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Mathematical Problems in Engineering
Volume 2014, Article ID 267843, 9 pages
http://dx.doi.org/10.1155/2014/267843
Research Article

On Multi-Laplace Transform for Solving Nonlinear Partial Differential Equations with Mixed Derivatives

1Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa
2Department of Mathematical Sciences, North-West University, Mafikeng Campus, Mmabatho 2735, South Africa

Received 28 April 2014; Accepted 21 May 2014; Published 11 June 2014

Academic Editor: Hossein Jafari

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

A novel approach is proposed to deal with a class of nonlinear partial equations including integer and noninteger order derivative. This class of equations cannot be handled with any other commonly used analytical technique. The proposed method is based on the multi-Laplace transform. We solved as an example some complicated equations. Three illustrative examples are presented to confirm the applicability of the proposed method. We have presented in detail the stability, the convergence and the uniqueness analysis of some examples.