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Novel Analysis of Fractional‐Order Fifth‐Order Korteweg–de Vries Equations

Author

Listed:
  • Ahmed B. Khoshaim
  • Muhammad Naeem
  • Ali Akgul
  • Nejib Ghanmi
  • Shamsullah Zaland

Abstract

In this paper, the ρ‐homotopy perturbation transformation method was applied to analysis of fifth‐order nonlinear fractional Korteweg–de Vries (KdV) equations. This technique is the mixture form of the ρ‐Laplace transformation with the homotopy perturbation method. The purpose of this study is to demonstrate the validity and efficiency of this method. Furthermore, it is demonstrated that the fractional and integer‐order solutions close in on the exact result. The suggested technique was effectively utilized and was accurate and simple to use for a number of related engineering and science models.

Suggested Citation

  • Ahmed B. Khoshaim & Muhammad Naeem & Ali Akgul & Nejib Ghanmi & Shamsullah Zaland, 2022. "Novel Analysis of Fractional‐Order Fifth‐Order Korteweg–de Vries Equations," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:1883268
    DOI: 10.1155/2022/1883268
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    References listed on IDEAS

    as
    1. Meshari Alesemi & Naveed Iqbal & Ahmed A. Hamoud & C. Rajivganthi, 2022. "The Analysis of Fractional-Order Proportional Delay Physical Models via a Novel Transform," Complexity, Hindawi, vol. 2022, pages 1-13, February.
    2. Nehad Ali Shah & Ioannis Dassios & Essam R. El-Zahar & Jae Dong Chung, 2022. "An Efficient Technique of Fractional-Order Physical Models Involving ρ -Laplace Transform," Mathematics, MDPI, vol. 10(5), pages 1-16, March.
    3. Naveed Iqbal & Humaira Yasmin & Ali Rezaiguia & Jeevan Kafle & A. Othman Almatroud & Taher S. Hassan & Fairouz Tchier, 2021. "Analysis of the Fractional-Order Kaup–Kupershmidt Equation via Novel Transforms," Journal of Mathematics, Hindawi, vol. 2021, pages 1-13, December.
    4. Meshari Alesemi & Naveed Iqbal & Thongchai Botmart, 2022. "Novel Analysis of the Fractional-Order System of Non-Linear Partial Differential Equations with the Exponential-Decay Kernel," Mathematics, MDPI, vol. 10(4), pages 1-17, February.
    5. Meshari Alesemi & Naveed Iqbal & Ahmed A. Hamoud, 2022. "The Analysis of Fractional‐Order Proportional Delay Physical Models via a Novel Transform," Complexity, John Wiley & Sons, vol. 2022(1).
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