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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 380484, 9 pages
http://dx.doi.org/10.1155/2013/380484
Research Article

Analytical Solutions of Boundary Values Problem of 2D and 3D Poisson and Biharmonic Equations by Homotopy Decomposition Method

1Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa
2Department of Mathematics and Institute for Mathematical Research, University of Putra Malaysia, 43400 Serdang, Selangor, Malaysia

Received 13 June 2013; Accepted 18 August 2013

Academic Editor: Santanu Saha Ray

Copyright © 2013 Abdon Atangana and Adem Kılıçman. 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.

Citations to this Article [5 citations]

The following is the list of published articles that have cited the current article.

  • Carlo Cattani, Hossein Jafari, and Xiao-Jun Yang, “Analytical Solutions of the One-Dimensional Heat Equations Arising in Fract al Transient Conduction with Local Fractional Derivative,” Abstract and Applied Analysis, 2013. View at Publisher · View at Google Scholar
  • Abdon Atangana, “Convergence and stability analysis of a novel iteration method for fractional biological population equation,” Neural Computing and Applications, 2014. View at Publisher · View at Google Scholar
  • Shun-Qin Wang, Yong-Ju Yang, and Hassan Kamil Jassim, “Local Fractional Function Decomposition Method for Solving Inhomogeneous Wave Equations with Local Fractional Derivative,” Abstract and Applied Analysis, vol. 2014, pp. 1–7, 2014. View at Publisher · View at Google Scholar
  • Chun-Guang Zhao, Ai-Min Yang, Hossein Jafari, and Ahmad Haghbin, “The Yang-Laplace Transform for Solving the IVPs with Local Fractional Derivative,” Abstract and Applied Analysis, vol. 2014, pp. 1–5, 2014. View at Publisher · View at Google Scholar
  • Abdon Atangana, Aden Ahmed, and Suares Clovis Oukouomi Noutchie, “On the Hamilton-Jacobi-Bellman Equation by the Homotopy Perturbation Method,” Abstract and Applied Analysis, vol. 2014, pp. 1–8, 2014. View at Publisher · View at Google Scholar