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Analysis of Homotopy Perturbation Method for Solving Fractional Order Differential Equations

Author

Listed:
  • Shumaila Javeed

    (Department of Mathematics, COMSATS University Islamabad, Park Road, 45550 Chak Shahzad Islamabad, Pakistan)

  • Dumitru Baleanu

    (Department of Mathematics, Cankaya University, 06790 Ankara, Turkey
    Institute of Space Sciences, 077125 Magurele-Bucharest, Romania)

  • Asif Waheed

    (Department of Mathematics, COMSATS University Islamabad, Kamra Rd, Attock, Punjab 43600, Pakistan)

  • Mansoor Shaukat Khan

    (Department of Mathematics, COMSATS University Islamabad, Park Road, 45550 Chak Shahzad Islamabad, Pakistan)

  • Hira Affan

    (Department of Physics, COMSATS University Islamabad, Park Road, 45550 Chak Shahzad Islamabad, Pakistan)

Abstract

The analysis of Homotopy Perturbation Method (HPM) for the solution of fractional partial differential equations (FPDEs) is presented. A unified convergence theorem is given. In order to validate the theory, the solution of fractional-order Burger-Poisson (FBP) equation is obtained. Furthermore, this work presents the method to find the solution of FPDEs, while the same partial differential equation (PDE) with ordinary derivative i.e., for α = 1 , is not defined in the given domain. Moreover, HPM is applied to a complicated obstacle boundary value problem (BVP) of fractional order.

Suggested Citation

  • Shumaila Javeed & Dumitru Baleanu & Asif Waheed & Mansoor Shaukat Khan & Hira Affan, 2019. "Analysis of Homotopy Perturbation Method for Solving Fractional Order Differential Equations," Mathematics, MDPI, vol. 7(1), pages 1-14, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:1:p:40-:d:194714
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    References listed on IDEAS

    as
    1. Wang, Qi, 2008. "Homotopy perturbation method for fractional KdV-Burgers equation," Chaos, Solitons & Fractals, Elsevier, vol. 35(5), pages 843-850.
    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. Mohamed. Z. Mohamed & Mohammed Yousif & Amjad E. Hamza, 2022. "Solving Nonlinear Fractional Partial Differential Equations Using the Elzaki Transform Method and the Homotopy Perturbation Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2022(1).
    2. Mohamed M. Mousa & Fahad Alsharari, 2021. "Convergence and Error Estimation of a New Formulation of Homotopy Perturbation Method for Classes of Nonlinear Integral/Integro-Differential Equations," Mathematics, MDPI, vol. 9(18), pages 1-14, September.
    3. Mehari Fentahun Endalew & Xiaoming Zhang, 2025. "Application of Modified Laplace Variational Iteration Hybrid Approach for Solving Time‐Fractional Fourth‐Order Parabolic PDEs," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).

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