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Keywords = time-fractional higher order KdV equations

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20 pages, 1115 KB  
Article
A Novel Computational Framework for Time-Fractional Higher-Order KdV Models: CLADM-Based Solutions and Comparative Analysis
by Priti V. Tandel, Anant Patel and Trushitkumar Patel
Axioms 2025, 14(7), 511; https://doi.org/10.3390/axioms14070511 - 1 Jul 2025
Viewed by 303
Abstract
This study applies the Conformable Laplace Adomian Decomposition Method (CLADM) to solve generalized time-fractional Korteweg–de Vries (KdV) models, including seventh- and fifth-order models. CLADM combines the conformable fractional derivative and Laplace transform with the Adomian decomposition technique, offering analytic approximate solutions. Numerical and [...] Read more.
This study applies the Conformable Laplace Adomian Decomposition Method (CLADM) to solve generalized time-fractional Korteweg–de Vries (KdV) models, including seventh- and fifth-order models. CLADM combines the conformable fractional derivative and Laplace transform with the Adomian decomposition technique, offering analytic approximate solutions. Numerical and graphical results, generated using MATLAB R2020a 9.8.0.1323502, validate the method’s efficiency and precision in capturing fractional-order dynamics. Fractional parameters ϱ significantly influence wave behavior, with higher orders yielding smoother profiles and reduced oscillations. Comparative analysis confirms CLADM’s superiority over existing methods in minimizing errors. The versatility of CLADM highlights its potential for studying nonlinear wave phenomena in diverse applications. Full article
(This article belongs to the Special Issue Fractional Calculus and Applied Analysis, 2nd Edition)
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