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Comparative qualitative analysis and numerical solution of conformable fractional derivative generalized KdV-mKdV equation

Author

Listed:
  • Rajeev Kumar

    (Maharishi Markandeshwar (Deemed to be University))

  • Rahul Dharra

    (Maharishi Markandeshwar (Deemed to be University))

  • Sanjeev Kumar

    (Thapar Institute of Engineering and Technology)

Abstract

The purpose of this article to study the conformal derivative form of nonlinear fractional partial differential equation. The time fractional generalized KdV-mKdV equation with higher order nonlinear terms is taken to utlize the concept of conformal derivative and Leibnitz rule for finding the wave solutions. The theory of bifurcation analysis is applied for the qualitative analysis of this equation to study the stability nature at the different critical points. The solutions obtained by the method of $$\frac{G^{'}}{G}$$ G ′ G represents graphically. The numerical classical Runge Kutta fourth order technique is implemented computationally to manifest the results which shows a good agreement with the obtained analytical solutions.

Suggested Citation

  • Rajeev Kumar & Rahul Dharra & Sanjeev Kumar, 2023. "Comparative qualitative analysis and numerical solution of conformable fractional derivative generalized KdV-mKdV equation," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 14(4), pages 1247-1254, August.
    • Handle: RePEc:spr:ijsaem:v:14:y:2023:i:4:d:10.1007_s13198-023-01928-x
    DOI: 10.1007/s13198-023-01928-x
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    References listed on IDEAS

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    1. Rajan Arora & Hariom Sharma, 2018. "Application of HAM to seventh order KdV equations," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 9(1), pages 131-138, February.
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