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Iterative Investigation Of Korteweg–De Vries Equation Using Ab Derivative In Caputo Sense

Author

Listed:
  • HUSSAM ALRABAIAH

    (Al Ain University, Al Ain, UAE2Mathematics Department, Tafila Technical University, Tafila, Jordan)

  • ZAHID ULLAH

    (Department of Mathematics, G. P. G. Jehanzeb College Saidu Sharif, Swat, KPK, Pakistan)

  • ISRAR AHMAD

    (Department of Mathematics, G. P. G. Jehanzeb College Saidu Sharif, Swat, KPK, Pakistan)

  • KHURSHEED J. ANSARI

    (Department of Mathematics, College of Science, King Khalid University, 61413 Abha, Saudi Arabia)

  • DONG QIU

    (School of Mathematics and Information Science, Guangxi University, No. 100 East University Road, Nanning 530004, P. R. China6College of Science, Chongqing University of Posts and Telecommunications, Nanan 400065, Chongqing, P. R. China)

  • FUAD S. AL-DUAIS

    (Department of Mathematics, College of Science and Humanities in Al-Aflaj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia8Administrative Department, Administrative Science College, Thamar University, Thamar 87246, Yemen)

Abstract

This paper is devoted to investigate Korteweg–De Vries equations (KDVEs) with third order under fractional Atangana–Baleanu–Caputo (ABC) derivative. We use an analytical method due to the Laplace transform and the Adomian decomposition technique. We establish the convergence analysis results for the considered problem by using nonlinear functional analysis. First of all, a general algorithm is developed for the computation of the required analytical approximate solution by using the mentioned method. By applying the developed algorithm, we then investigate the approximate solutions for some examples. The computed solution has also been presented graphically using Matlab. Laplace Adomian decomposition method (LADM) is a powerful full technique that is easy to implement. In addition, the said method has also a fast convergent quality.

Suggested Citation

  • Hussam Alrabaiah & Zahid Ullah & Israr Ahmad & Khursheed J. Ansari & Dong Qiu & Fuad S. Al-Duais, 2023. "Iterative Investigation Of Korteweg–De Vries Equation Using Ab Derivative In Caputo Sense," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(10), pages 1-12.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:10:n:s0218348x23400959
    DOI: 10.1142/S0218348X23400959
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