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

Rajeev Kumar (), Rahul Dharra () and Sanjeev Kumar ()
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Rajeev Kumar: Maharishi Markandeshwar (Deemed to be University)
Rahul Dharra: Maharishi Markandeshwar (Deemed to be University)
Sanjeev Kumar: Thapar Institute of Engineering and Technology

International Journal of System Assurance Engineering and Management, 2023, vol. 14, issue 4, No 8, 1247-1254

Abstract: 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.

Keywords: Conformal derivatives; Bifurcation; Traveling wave solution; Runge Kutta method; KdV-mKdV equation (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13198-023-01928-x

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