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Solving Nonlinear Fractional Partial Differential Equations Using the Elzaki Transform Method and the Homotopy Perturbation Method

Author

Listed:
  • Mohamed. Z. Mohamed
  • Mohammed Yousif
  • Amjad E. Hamza

Abstract

In this paper, we combine the Elzaki transform method (ETM) with the new homotopy perturbation method (NHPM) for the first time. This hybrid approach can solve initial value problems numerically and analytically, such as nonlinear fractional differential equations of various normal orders. The Elzaki transform method (ETM) is used to solve nonlinear fractional differential equations, and then the homotopy is applied to the transformed equation, which includes the beginning conditions. To obtain the solution to an equation, we use the inverse transforms of the Elzaki transform method (ETM). The initial conditions have a big impact on the equation’s result. We give three beginning value issues that were solved as precise or approximation solutions with high rigor to demonstrate the method’s power and correctness. It is clear that solving nonlinear partial differential equations with the crossbred approach is the best alternative.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2022:y:2022:i:1:n:4743234
    DOI: 10.1155/2022/4743234
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    References listed on IDEAS

    as
    1. Mohamed Z. Mohamed & Tarig M. Elzaki & Mohamed S. Algolam & Eltaib M. Abd Elmohmoud & Amjad E. Hamza, 2021. "New Modified Variational Iteration Laplace Transform Method Compares Laplace Adomian Decomposition Method for Solution Time-Partial Fractional Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2021, pages 1-10, March.
    2. Mohamed Z. Mohamed & Tarig M. Elzaki & Mohamed S. Algolam & Eltaib M. Abd Elmohmoud & Amjad E. Hamza, 2021. "New Modified Variational Iteration Laplace Transform Method Compares Laplace Adomian Decomposition Method for Solution Time‐Partial Fractional Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2021(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. 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.
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    Cited by:

    1. Asim Zafar & Waseem Razzaq & Abdullah Nazir & Mohammed Ahmed Alomair & Abdulaziz S. Al Naim & Abdulrahman Alomair, 2025. "Bifurcation Analysis and Solitons Dynamics of the Fractional Biswas–Arshed Equation via Analytical Method," Mathematics, MDPI, vol. 13(19), pages 1-22, October.

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