A FRACTAL SOLUTION OF CAMASSA–HOLM AND DEGASPERIS–PROCESI MODELS UNDER TWO-SCALE DIMENSION APPROACH

Fenglian Liu, Shu Wang and Muhammad Nadeem
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Fenglian Liu: Institute of Land & Resources and Sustainable Development, Yunnan University of Finance and Economics, Kunming 650221, P. R. China
Shu Wang: Institute of Land & Resources and Sustainable Development, Yunnan University of Finance and Economics, Kunming 650221, P. R. China
Muhammad Nadeem: School of Mathematics and Statistics, Qujing Normal University, Qujing 655011, P. R. China

FRACTALS (fractals), 2023, vol. 31, issue 05, 1-10

Abstract: This study proposes a new method, called the Fractal Yang transform method (F𠒴TM), for obtaining the fractal solution of the modified Camassa–Holm (mCH) and Degasperis–Procesi (mDP) models with fractal derivatives. The authors use the two-scale fractal approach to convert the fractal problem into its differential components and implement the Yang transform (𠒴T) to achieve the recurrence iteration. We then apply the homotopy perturbation method (HPM) to overcome the difficulty of nonlinear elements in the recurrence iteration, which makes it simple to acquire further iterations. The most advantage of this fractal approach is that it has no restriction on variables and provides successive iterations. The fractal results are presented in the sense of a series that converges to the exact solution only after a few iteration. Graphical behavior demonstrates that this fractal approach is a very fast and remarkable solution, particularly with fractal derivatives.

Keywords: Yang Transform; Homotopy Perturbation Method; mCH and mDP Models; Fractal Solution (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23500536

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