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Variational Approximate Solutions of Fractional Nonlinear Nonhomogeneous Equations with Laplace Transform

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  • Yanqin Liu
  • Fengsheng Xu
  • Xiuling Yin

Abstract

A novel modification of the variational iteration method is proposed by means of Laplace transform and homotopy perturbation method. The fractional lagrange multiplier is accurately determined by the Laplace transform and the nonlinear one can be easily handled by the use of He’s polynomials. Several fractional nonlinear nonhomogeneous equations are analytically solved as examples and the methodology is demonstrated.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:819268
    DOI: 10.1155/2013/819268
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    References listed on IDEAS

    as
    1. Odibat, Zaid & Momani, Shaher, 2008. "Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 167-174.
    2. Yanqin Liu, 2012. "Variational Homotopy Perturbation Method for Solving Fractional Initial Boundary Value Problems," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-10, June.
    3. Yanqin Liu, 2012. "Variational Homotopy Perturbation Method for Solving Fractional Initial Boundary Value Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. Yanqin Liu, 2012. "Approximate Solutions of Fractional Nonlinear Equations Using Homotopy Perturbation Transformation Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    5. Yanqin Liu, 2012. "Approximate Solutions of Fractional Nonlinear Equations Using Homotopy Perturbation Transformation Method," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-14, April.
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