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Modified Homotopy Perturbation Method for Solving Fractional Differential Equations

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  • A. A. Hemeda

Abstract

The modified homotopy perturbation method is extended to derive the exact solutions for linear (nonlinear) ordinary (partial) differential equations of fractional order in fluid mechanics. The fractional derivatives are taken in the Caputo sense. This work will present a numerical comparison between the considered method and some other methods through solving various fractional differential equations in applied fields. The obtained results reveal that this method is very effective and simple, accelerates the rapid convergence of the series solution, and reduces the size of work to only one iteration.

Suggested Citation

  • A. A. Hemeda, 2014. "Modified Homotopy Perturbation Method for Solving Fractional Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:594245
    DOI: 10.1155/2014/594245
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    References listed on IDEAS

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    1. Abbasbandy, S., 2007. "Application of He’s homotopy perturbation method to functional integral equations," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1243-1247.
    2. A. A. Hemeda, 2012. "Formulation and Solution of nth‐Order Derivative Fuzzy Integrodifferential Equation Using New Iterative Method with a Reliable Algorithm," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. He, Ji-Huan, 2005. "Application of homotopy perturbation method to nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 695-700.
    4. Hemeda, A.A., 2009. "Variational iteration method for solving non-linear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1297-1303.
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    1. Pratibha Verma & Wojciech Sumelka, 2025. "Existence, Stability, and Numerical Methods for Multi-Fractional Integro-Differential Equations with Singular Kernel," Mathematics, MDPI, vol. 13(16), pages 1-38, August.

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