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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 752869, 14 pages
Approximate Solutions of Fractional Nonlinear Equations Using Homotopy Perturbation Transformation Method
1Department of Mathematics, Dezhou University, Dezhou 253023, China
2Nonlinear Dynamics and Chaos Group, School of Management, Tianjin University, Tianjin 30072, China
Received 11 November 2011; Revised 25 December 2011; Accepted 30 January 2012
Academic Editor: Muhammad Aslam Noor
Copyright © 2012 Yanqin Liu. 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 [15 citations]
The following is the list of published articles that have cited the current article.
- Łukasz Płociniczak, and Hanna Okrasińska, “Approximate self-similar solutions to a nonlinear diffusion equation with time-fractional derivative,” Physica D: Nonlinear Phenomena, 2013.
- Li-Mei Yan, “Modified Homotopy Perturbation Method Coupled With Laplace Transform For Fractional Heat Transfer And Porous Media Equations,” Thermal Science, vol. 17, no. 5, pp. 1409–1414, 2013.
- Limei Yan, “Numerical Solutions of Fractional Fokker-Planck Equations Using Iterative Laplace Transform Method,” Abstract and Applied Analysis, 2013.
- Yanqin Liu, Fengsheng Xu, and Xiuling Yin, “Variational Approximate Solutions of Fractional Nonlinear Nonhomogeneous Equations with Laplace Transform,” Abstract and Applied Analysis, vol. 2013, pp. 1–9, 2013.
- Yanqin Liu, and Limei Yan, “Solutions of Fractional Konopelchenko-Dubrovsky and Nizhnik-Novikov-Veselov Equations Using a Generalized Fractional Subequation Method,” Abstract and Applied Analysis, vol. 2013, pp. 1–7, 2013.
- Hong-Yan Liu, Ji-Huan He, and Zheng-Biao Li, “Fractional calculus for nanoscale flow and heat transfer,” International Journal of Numerical Methods for Heat & Fluid Flow, vol. 24, no. 6, pp. 1227–1250, 2014.
- Ji-Huan He, “A Tutorial Review on Fractal Spacetime and Fractional Calculus,” International Journal of Theoretical Physics, vol. 53, no. 11, pp. 3698–3718, 2014.
- Gilberto Gonzalez-Parra, Abraham J. Arenas, and Benito M. Chen-Charpentier, “A fractional order epidemic model for the simulation of outbreaks of influenza A(H1N1),” Mathematical Methods in The Applied Sciences, vol. 37, no. 15, pp. 2218–2226, 2014.
- M. A. Mohamed, and M. Sh. Torky, “Approximate Solution of Fractional Nonlinear Partial Differential Equations by the Legendre Multiwavelet Galerkin Method,” Journal of Applied Mathematics, vol. 2014, pp. 1–12, 2014.
- Xiu-Fen Gu, Qiu-Ya Wang, Meng Zhang, and Yan-Qin Liu, “Approximate Solutions Of Fractional Non-Linear Evolution Equations,” Thermal Science, vol. 18, no. 5, pp. 1553–1556, 2014.
- Abraham J. Arenas, Gilberto González-Parra, and Benito M. Chen-Charpentier, “Construction of nonstandard finite difference schemes for the SI and SIR epidemic models of fractional order,” Mathematics and Computers in Simulation, 2015.
- S. Saha Ray, and S. Sahoo, “A comparative study on the analytic solutions of fractional coupled sine-Gordon equations by using two reliable methods,” Applied Mathematics And Computation, vol. 253, pp. 72–82, 2015.
- Yanqin Liu, and Lihua Dong, “Approximate solutions of multi-order fractional advection-dispersion equation with non-polynomial conditions,” International Journal of Numerical Methods for Heat & Fluid Flow, vol. 25, no. 1, pp. 57–67, 2015.
- Ming-Feng Zhang, Yan-Qin Liu, and Xiao-Shuang Zhou, “Efficient Homotopy Perturbation Method For Fractional Non-Linear Equations Using Sumudu Transform,” Thermal Science, vol. 19, no. 4, pp. 1167–1171, 2015.
- U. Filobello-Nino, H. Vazquez-Leal, A. Sarmiento-Reyes, J. Cervantes-Perez, A. Perez-Sesma, V.M. Jimenez-Fernandez, D. Pereyra-Diaz, J. Huerta Chua, L.J. Morales-Mendoza, M. Gonzalez-Lee, and F. Castro-Gonzalez, “Laplace transform-homotopy perturbation method with arbitrary initial approximation and residual error cancelation.,” Applied Mathematical Modelling, 2016.