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Approximate Solutions of Fractional Nonlinear Equations Using Homotopy Perturbation Transformation Method

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  • Yanqin Liu

Abstract

A homotopy perturbation transformation method (HPTM) which is based on homotopy perturbation method and Laplace transform is first applied to solve the approximate solution of the fractional nonlinear equations. The nonlinear terms can be easily handled by the use of He′s polynomials. Illustrative examples are included to demonstrate the high accuracy and fast convergence of this new algorithm.

Suggested Citation

  • Yanqin Liu, 2012. "Approximate Solutions of Fractional Nonlinear Equations Using Homotopy Perturbation Transformation Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:752869
    DOI: 10.1155/2012/752869
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    References listed on IDEAS

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    1. Ghorbani, Asghar, 2009. "Beyond Adomian polynomials: He polynomials," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1486-1492.
    2. He, Ji-Huan, 2005. "Application of homotopy perturbation method to nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 695-700.
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    Cited by:

    1. Saha Ray, S. & Sahoo, S., 2015. "A comparative study on the analytic solutions of fractional coupled sine–Gordon equations by using two reliable methods," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 72-82.
    2. Hegagi Mohamed Ali & Ismail Gad Ameen, 2019. "An Efficient Approach for Solving Fractional Dynamics of a Predator-Prey System," Modern Applied Science, Canadian Center of Science and Education, vol. 13(11), pages 116-116, November.
    3. Arenas, Abraham J. & González-Parra, Gilberto & Chen-Charpentier, Benito M., 2016. "Construction of nonstandard finite difference schemes for the SI and SIR epidemic models of fractional order," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 121(C), pages 48-63.
    4. Yanqin Liu & Fengsheng Xu & Xiuling Yin, 2013. "Variational Approximate Solutions of Fractional Nonlinear Nonhomogeneous Equations with Laplace Transform," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. Limei Yan, 2013. "Numerical Solutions of Fractional Fokker‐Planck Equations Using Iterative Laplace Transform Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    6. M. A. Mohamed & M. Sh. Torky, 2014. "Approximate Solution of Fractional Nonlinear Partial Differential Equations by the Legendre Multiwavelet Galerkin Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    7. Yanqin Liu & Limei Yan, 2013. "Solutions of Fractional Konopelchenko‐Dubrovsky and Nizhnik‐Novikov‐Veselov Equations Using a Generalized Fractional Subequation Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    8. Benito Chen-Charpentier & Gilberto González-Parra & Abraham J. Arenas, 2016. "Fractional Order Financial Models for Awareness and Trial Advertising Decisions," Computational Economics, Springer;Society for Computational Economics, vol. 48(4), pages 555-568, December.

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