Semi-Analytic Scheme for Fractional Insight into Multi-Component KdV System Arises in Water Wave Mechanism

Document Type : Research Paper

Authors
Shelly Arora 1
Wen Xiu Ma 2 , 3 , 4 , 5
Sukhjit Singh Dhaliwal 6
Atul Pasrija 1
1 Department of Mathematics, Punjabi University, Patiala, 147002, India
2 Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, Zhejiang, PR China
3 Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia
4 Department of Mathematics and Statistics, University of South Florida, Tampa, 33620-5700, USA
5 Material Science Innovation and Modelling, Department of Mathematical sciences, North-West University, Mafikeng Campus, Mmabatho, 2735, South Africa
6 Department of Mathematics, SLIET, Longowal, Sangrur, 148106, Punjab, India
10.22055/jacm.2025.48506.5285
Abstract
The present study aims to broaden the applications of a newly emerged Laplace-like transform known as the generalized bivariate integral transform. This transform is combined with the homotopy perturbation method to obtain approximate and analytic solutions for the fractional multi-component Korteweg-de Vries system. The time fractional derivative is considered in the conformable sense.  The scheme involves the applications of generalized bivariate transform and its inversion to handle fractional operator. He's polynomials, associated with homotopy perturbation method, are employed to decompose the non-linearity of the proposed problem. Through the combination of these two powerful tools, an iterative expression is derived to compute the components of a rapidly convergent series solution. A rigorous analysis is conducted, and sufficient conditions for convergence are presented in detail. The proposed procedure effectively demonstrates distinct soliton mechanisms under various of initial conditions for proposed fractional system. The novelty of this study lies in the first-time application of the proposed scheme to a conformable fractional system. A key highlight of the study is the convergence behavior for non-integer order derivatives to study soliton behavior even in the absence of a known exact solution.
Keywords
Generalized bivariate transform
Homotopy perturbation method
Semi-analytic scheme
KdV-system
Conformable fractional derivative
Subjects

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Journal of Applied and Computational Mechanics
Volume 12, Issue 2
Spring 2026
Pages 632-647