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Analytical Solution of the Local Fractional KdV Equation

Author

Listed:
  • Kholoud Saad Albalawi

    (Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University, Riyadh 11566, Saudi Arabia)

  • Ibtehal Alazman

    (Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University, Riyadh 11566, Saudi Arabia)

  • Jyoti Geetesh Prasad

    (MKSSS’s Cummins College of Engineering for Women, Pune 411052, India
    Department of Mathematics, AMITY School of Applied Sciences, AMITY University Rajasthan, Jaipur 302002, India)

  • Pranay Goswami

    (School of Liberal Studies, Dr B. R. Ambedkar University Delhi, Delhi 110006, India)

Abstract

This research work is dedicated to solving the n-generalized Korteweg–de Vries (KdV) equation in a fractional sense. The method is a combination of the Sumudu transform and the Adomian decomposition method. This method has significant advantages for solving differential equations that are both linear and nonlinear. It is easy to find the solutions to fractional-order PDEs with less computing labor.

Suggested Citation

  • Kholoud Saad Albalawi & Ibtehal Alazman & Jyoti Geetesh Prasad & Pranay Goswami, 2023. "Analytical Solution of the Local Fractional KdV Equation," Mathematics, MDPI, vol. 11(4), pages 1-13, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:882-:d:1063393
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    References listed on IDEAS

    as
    1. Alexander Sukhinov & Alexander Chistyakov & Elena Timofeeva & Alla Nikitina & Yulia Belova, 2022. "The Construction and Research of the Modified “Upwind Leapfrog” Difference Scheme with Improved Dispersion Properties for the Korteweg–de Vries Equation," Mathematics, MDPI, vol. 10(16), pages 1-15, August.
    2. Saad Althobaiti & Ravi Shanker Dubey & Jyoti Geetesh Prasad, 2022. "Solution Of Local Fractional Generalized Fokker–Planck Equation Using Local Fractional Mohand Adomian Decomposition Method," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-9, February.
    3. Alexander Sukhinov & Alexander Chistyakov & Inna Kuznetsova & Yulia Belova & Elena Rahimbaeva, 2022. "Development and Research of a Modified Upwind Leapfrog Scheme for Solving Transport Problems," Mathematics, MDPI, vol. 10(19), pages 1-21, September.
    4. Salehi, Younes & Darvishi, Mohammad T. & Schiesser, William E., 2018. "Numerical solution of space fractional diffusion equation by the method of lines and splines," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 465-480.
    5. Owolabi, Kolade M. & Atangana, Abdon, 2017. "Numerical approximation of nonlinear fractional parabolic differential equations with Caputo–Fabrizio derivative in Riemann–Liouville sense," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 171-179.
    Full references (including those not matched with items on IDEAS)

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