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Variational Homotopy Perturbation Method for Solving Fractional Initial Boundary Value Problems

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  • Yanqin Liu

Abstract

A variational homotopy perturbation method (VHPM) which is based on variational iteration method and homotopy perturbation method is applied to solve the approximate solution of the fractional initial boundary value problems. The nonlinear terms can be easily handled by the use of He′s polynomials. It is observed that the variational iteration method is very efficient and easier to implements; illustrative examples are included to demonstrate the high accuracy and fast convergence of this new algorithm.

Suggested Citation

  • Yanqin Liu, 2012. "Variational Homotopy Perturbation Method for Solving Fractional Initial Boundary Value Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:727031
    DOI: 10.1155/2012/727031
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    References listed on IDEAS

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    1. Syed Tauseef Mohyud-Din & Ahmet Yildirim & M. M. Hosseini, 2010. "Variational Iteration Method for Initial and Boundary Value Problems Using He's Polynomials," International Journal of Differential Equations, Hindawi, vol. 2010, pages 1-28, April.
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    Cited by:

    1. Ji-Huan He, 2012. "Comment on “Variational Iteration Method for Fractional Calculus Using He’s Polynomials”," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Y. Y. Lee, 2012. "Analysis of the Nonlinear Structural‐Acoustic Resonant Frequencies of a Rectangular Tube with a Flexible End Using Harmonic Balance and Homotopy Perturbation Methods," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. 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).
    4. 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).
    5. 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).
    6. Rabab Alyusof & Shams Alyusof & Naveed Iqbal & Mohammad Asif Arefin, 2022. "Novel Evaluation of the Fractional Acoustic Wave Model with the Exponential‐Decay Kernel," Complexity, John Wiley & Sons, vol. 2022(1).

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