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Differential Equations and Nonlinear Mechanics
Volume 2008, Article ID 686512, 16 pages
Research Article

Series Solutions of Time-Fractional PDEs by Homotopy Analysis Method

Centre for Modelling and Data Analysis, School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor, Malaysia

Received 12 August 2008; Accepted 30 October 2008

Academic Editor: Shijun Liao

Copyright © 2008 O. Abdulaziz et al. 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 [9 citations]

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

  • Manoj N. Mehta, Kajal K. Patel, and Twinkle R. Singh, “Solution of one dimensional ground water recharge phenomenon by homotopy analysis method,” 2013 Nirma University International Conference on Engineering (NUiCONE), pp. 1–6, . View at Publisher · View at Google Scholar
  • R. Yulita Molliq, M.S.M. Noorani, I. Hashim, and R.R. Ahmad, “Approximate solutions of fractional Zakharov–Kuznetsov equations by VIM,” Journal of Computational and Applied Mathematics, vol. 233, no. 2, pp. 103–108, 2009. View at Publisher · View at Google Scholar
  • Sandile Sydney Motsa, Stanford Shateyi, Gerald T. Marewo, and Precious Sibanda, “An improved spectral homotopy analysis method for MHD flow in a semi-porous channel,” Numerical Algorithms, vol. 60, no. 3, pp. 463–481, 2011. View at Publisher · View at Google Scholar
  • Muhammet Kurulay, “Solving the fractional nonlinear Klein-Gordon equation by means of the homotopy analysis method,” Advances in Difference Equations, 2012. View at Publisher · View at Google Scholar
  • Mehmet Giyas Sakar, and Fevzi Erdogan, “The homotopy analysis method for solving the time-fractional Fornberg-Whitham equation and comparison with Adomian's decomposition method,” Applied Mathematical Modelling, vol. 37, no. 20-21, pp. 8876–8885, 2013. View at Publisher · View at Google Scholar
  • B. A. Jacobs, and C. Harley, “Two Hybrid Methods for Solving Two-Dimensional Linear Time-Fractional Partial Differential Equations,” Abstract and Applied Analysis, vol. 2014, pp. 1–10, 2014. View at Publisher · View at Google Scholar
  • Byron A. Jacobs, “High-order compact finite difference and laplace transform method for the solution of time-fractional heat equations with dirchlet and neumann boundary conditions,” Numerical Methods for Partial Differential Equations, 2015. View at Publisher · View at Google Scholar
  • Gómez-Aguilar, Reyes, Torres, Yépez-Martínez, Baleanu, and Sosa, “Fractional Liénard type model of a pipeline within the fractional derivative without singular kernel,” Advances in Difference Equations, vol. 2016, no. 1, 2016. View at Publisher · View at Google Scholar
  • Eman Abuteen, Asad Freihat, Hammad Khalil, Rahmat Ali Khan, and Mohammed Al-Smadi, “Approximate series solution of nonlinear, fractional Klein-Gordon equations using fractional reduced differential transform method,” Journal of Mathematics and Statistics, vol. 12, no. 1, pp. 23–33, 2016. View at Publisher · View at Google Scholar