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Soliton Solutions of Generalized Third Order Time‐Fractional KdV Models Using Extended He‐Laplace Algorithm

Author

Listed:
  • Mubashir Qayyum
  • Efaza Ahmad
  • Sidra Afzal
  • Saraswati Acharya

Abstract

In this research, the He‐Laplace algorithm is extended to generalized third order, time‐fractional, Korteweg‐de Vries (KdV) models. In this algorithm, the Laplace transform is hybrid with homotopy perturbation and extended to highly nonlinear fractional KdVs, including potential and Burgers KdV models. Time‐fractional derivatives are taken in Caputo sense throughout the manuscript. Convergence and error estimation are confirmed theoretically as well as numerically for the current model. Numerical convergence and error analysis is also performed by computing residual errors in the entire fractional domain. Graphical illustrations show the effect of fractional parameter on the solution as 2D and 3D plots. Analysis reveals that the He‐Laplace algorithm is an efficient approach for time‐fractional models and can be used for other families of equations.

Suggested Citation

  • Mubashir Qayyum & Efaza Ahmad & Sidra Afzal & Saraswati Acharya, 2022. "Soliton Solutions of Generalized Third Order Time‐Fractional KdV Models Using Extended He‐Laplace Algorithm," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:2174806
    DOI: 10.1155/2022/2174806
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    1. Ilyas Khan & Aisha M. Alqahtani & Arshad Khan & Dolat Khan & Abdul Hamid Ganie & Gohar Ali, 2022. "New Results Of Fractal Fractional Model Of Drilling Nanoliquids With Clay Nanoparticles," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-9, February.
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