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Analysis of the Fuzzy Fractional‐Order Solitary Wave Solutions for the KdV Equation in the Sense of Caputo‐Fabrizio Derivative

Author

Listed:
  • Muhammad Naeem
  • Hadi Rezazadeh
  • Ahmed A. Khammash
  • Rasool Shah
  • Shamsullah Zaland

Abstract

In this paper, we construct a system for analysis of an analytic solution of fractional fuzzy solitary wave solutions for the Korteweg–De Vries (KdV) equation. We apply the iterative method and the Laplace transform under the fractional Caputo‐Fabrizio operator. The obtained series form the solution was calculated and approached the estimate values of the proposed problems. The upper and lower portions of the fuzzy result in all three problems were simulation applying two different fractional order among zero and one. The fractional operator is nonsingular and global since the exponential function is present. It provides all types of fuzzy results occurring among zero and one at any fractional order because its dynamic behaviour is globalised of the suggested problems. Because the fuzzy number provides the result in a fuzzy form, with lower and upper branches, fuzziness is also incorporated in the unknown quantity.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:3688916
    DOI: 10.1155/2022/3688916
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    References listed on IDEAS

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    1. 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).
    2. 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.
    3. Noufe H. Aljahdaly & Ali Akgül & Rasool Shah & Ibrahim Mahariq & Jeevan Kafle & A. Ghareeb, 2022. "A Comparative Analysis of the Fractional-Order Coupled Korteweg–De Vries Equations with the Mittag–Leffler Law," Journal of Mathematics, Hindawi, vol. 2022, pages 1-30, February.
    4. 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.
    5. Kamsing Nonlaopon & Muhammad Naeem & Ahmed M. Zidan & Rasool Shah & Ahmed Alsanad & Abdu Gumaei & Muhammad Imran Asjad, 2021. "Numerical Investigation of the Time-Fractional Whitham–Broer–Kaup Equation Involving without Singular Kernel Operators," Complexity, Hindawi, vol. 2021, pages 1-21, July.
    6. Mohammed Kbiri Alaoui & Rabia Fayyaz & Adnan Khan & Rasool Shah & Mohammed S. Abdo & Fathalla A. Rihan, 2021. "Analytical Investigation of Noyes–Field Model for Time-Fractional Belousov–Zhabotinsky Reaction," Complexity, Hindawi, vol. 2021, pages 1-21, December.
    7. 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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    Cited by:

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