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A Comparative Analysis of the Fractional‐Order Coupled Korteweg–De Vries Equations with the Mittag–Leffler Law

Author

Listed:
  • Noufe H. Aljahdaly
  • Ali Akgül
  • Rasool Shah
  • Ibrahim Mahariq
  • Jeevan Kafle

Abstract

This article applies efficient methods, namely, modified decomposition method and new iterative transformation method, to analyze a nonlinear system of Korteweg–de Vries equations with the Atangana–Baleanu fractional derivative. The nonlinear fractional coupled systems investigated in this current analysis are the system of Korteweg–de Vries and the modified system of Korteweg–de Vries equations applied as a model in nonlinear physical phenomena arising in chemistry, biology, physics, and applied sciences. Approximate analytical results are represented in the form of a series with straightforward components, and some aspects showed an appropriate dependence on the values of the fractional‐order derivatives. The convergence and uniqueness analysis is carried out. To comprehend the analytical procedure of both methods, three test examples are provided for the analytical results of the time‐fractional KdV equation. Additionally, the efficiency of the mentioned procedures and the reduction in calculations provide broader applicability. It is also illustrated that the findings of the current methodology are in close harmony with the exact solutions. The series result achieved applying this technique is proved to be accurate and reliable with minimal calculations. The numerical simulations for obtained solutions are discussed for different values of the fractional order.

Suggested Citation

  • Noufe H. Aljahdaly & Ali Akgül & Rasool Shah & Ibrahim Mahariq & Jeevan Kafle, 2022. "A Comparative Analysis of the Fractional‐Order Coupled Korteweg–De Vries Equations with the Mittag–Leffler Law," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:8876149
    DOI: 10.1155/2022/8876149
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    References listed on IDEAS

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    1. Wenfeng He & Nana Chen & Ioannis Dassios & Nehad Ali Shah & Jae Dong Chung, 2021. "Fractional System of Korteweg-De Vries Equations via Elzaki Transform," Mathematics, MDPI, vol. 9(6), pages 1-18, March.
    2. Omar Abu Arqub & Mohamed S. Osman & Abdel-Haleem Abdel-Aty & Abdel-Baset A. Mohamed & Shaher Momani, 2020. "A Numerical Algorithm for the Solutions of ABC Singular Lane–Emden Type Models Arising in Astrophysics Using Reproducing Kernel Discretization Method," Mathematics, MDPI, vol. 8(6), pages 1-15, June.
    3. A. A. Alderremy & Hassan Khan & Rasool Shah & Shaban Aly & Dumitru Baleanu, 2020. "The Analytical Analysis of Time-Fractional Fornberg–Whitham Equations," Mathematics, MDPI, vol. 8(6), pages 1-14, June.
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    Cited by:

    1. Muhammad Naeem & Hadi Rezazadeh & Ahmed A. Khammash & Rasool Shah & Shamsullah Zaland, 2022. "Analysis of the Fuzzy Fractional‐Order Solitary Wave Solutions for the KdV Equation in the Sense of Caputo‐Fabrizio Derivative," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    2. Naveed Iqbal & Moteb Fheed Saad Al Harbi & Saleh Alshammari & Shamsullah Zaland, 2022. "Analysis of Fractional Differential Equations with the Help of Different Operators," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    3. Mounirah Areshi & Muhammad Naeem & Noorolhuda Wyal, 2022. "Analytical Investigation of Some Dynamical Systems by ZZ Transform with Mittag–Leffler Kernel," Complexity, John Wiley & Sons, vol. 2022(1).

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