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

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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 \(\frac{G^{'}}{G}\) 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.

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Authors and Affiliations

  1. Department of Mathematics, Maharishi Markandeshwar (Deemed to be University), Mullana, Ambala, Haryana, 133001, India

    Rajeev Kumar & Rahul Dharra

  2. Department of Mathematics, Thapar Institute of Engineering and Technology, Patiala, Punjab, 147001, India

    Sanjeev Kumar

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  1. Rajeev Kumar
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  2. Rahul Dharra
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  3. Sanjeev Kumar
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Correspondence to Rajeev Kumar.

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Kumar, R., Dharra, R. & Kumar, S. Comparative qualitative analysis and numerical solution of conformable fractional derivative generalized KdV-mKdV equation. Int J Syst Assur Eng Manag 14, 1247–1254 (2023). https://doi.org/10.1007/s13198-023-01928-x

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  • DOI: https://doi.org/10.1007/s13198-023-01928-x

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