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Fractional System of Korteweg-De Vries Equations via Elzaki Transform

Author

Listed:
  • Wenfeng He

    (College of Science, Hainan University, Haikou 570228, China)

  • Nana Chen

    (Faculty of Network, Haikou College of Economics, Haikou 571127, China)

  • Ioannis Dassios

    (AMPSAS, University College Dublin, D4 Dublin, Ireland)

  • Nehad Ali Shah

    (Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City 58307, Vietnam
    Faculty of Mathematics & Statistics, Ton Duc Thang University, Ho Chi Minh City 58307, Vietnam)

  • Jae Dong Chung

    (Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea)

Abstract

In this article, a hybrid technique, called the Iteration transform method, has been implemented to solve the fractional-order coupled Korteweg-de Vries (KdV) equation. In this method, the Elzaki transform and New Iteration method are combined. The iteration transform method solutions are obtained in series form to analyze the analytical results of fractional-order coupled Korteweg-de Vries equations. To understand the analytical procedure of Iteration transform method, some numerical problems are presented for the analytical result of fractional-order coupled Korteweg-de Vries equations. It is also demonstrated that the current technique’s solutions are in good agreement with the exact results. The numerical solutions show that only a few terms are sufficient for obtaining an approximate result, which is efficient, accurate, and reliable.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:6:p:673-:d:521546
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    References listed on IDEAS

    as
    1. Limei Yan, 2013. "Numerical Solutions of Fractional Fokker-Planck Equations Using Iterative Laplace Transform Method," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, December.
    2. Prakash, Amit & Kumar, Manoj & Baleanu, Dumitru, 2018. "A new iterative technique for a fractional model of nonlinear Zakharov–Kuznetsov equations via Sumudu transform," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 30-40.
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    Cited by:

    1. Attia Rani & Muhammad Shakeel & Mohammed Kbiri Alaoui & Ahmed M. Zidan & Nehad Ali Shah & Prem Junsawang, 2022. "Application of the Exp − φ ξ -Expansion Method to Find the Soliton Solutions in Biomembranes and Nerves," Mathematics, MDPI, vol. 10(18), pages 1-12, September.
    2. Mamta Kapoor & Nehad Ali Shah & Salman Saleem & Wajaree Weera, 2022. "An Analytical Approach for Fractional Hyperbolic Telegraph Equation Using Shehu Transform in One, Two and Three Dimensions," Mathematics, MDPI, vol. 10(12), pages 1-26, June.
    3. Muhammad Shakeel & Attaullah & Mohammed Kbiri Alaoui & Ahmed M. Zidan & Nehad Ali Shah & Wajaree Weera, 2022. "Closed-Form Solutions in a Magneto-Electro-Elastic Circular Rod via Generalized Exp-Function Method," Mathematics, MDPI, vol. 10(18), pages 1-21, September.
    4. Shumaila Naz & Attia Rani & Muhammad Shakeel & Nehad Ali Shah & Jae Dong Chung, 2022. "Novel Soliton Solutions of the Fractional Riemann Wave Equation via a Mathematical Method," Mathematics, MDPI, vol. 10(22), pages 1-21, November.

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