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Discontinuity, Nonlinearity, and Complexity 14(1) 75--99 | DOI:10.5890/DNC.2025.03.006

Mamta Kapoor, Simran Kour

Department of Mathematics, Lovely Professional University, Phagwara, Punjab, India-144411

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Abstract

In this paper, the applications of the Yang transformation technique are considered to deal with the non-linear fractional Korteweg-de Vries (KdV) equation and fractional coupled Korteweg-de Vries (CKdV) equation. The evolution and interaction of non-linear waves in diverse physical systems are described by the KdV equation. The suggested method yields approximate-analytical solutions in the form of a series that are symmetrically dependent on the values of fractional-order derivatives and have simple, understandable mechanics. The Caputo sense of fractional derivative is employed, and the convergence and uniqueness of the methods are analysed. Five test examples are offered to demonstrate the analytical procedure of the technique and it is demonstrated that the proposed techniques are efficient and reduce the number of calculations required. The results obtained from the methods are shown to be in concurrency with exact solutions, and the suggested techniques are deemed powerful for solving non-linear fractional PDEs.

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