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YANG TRANSFORM FOR THE HOMOTOPY PERTURBATION METHOD: PROMISE FOR FRACTAL-FRACTIONAL MODELS

MUHAMMAD NADEEM

https://orcid.org/0000-0002-9349-4729

School of Mathematics and Statistics, Qujing Normal University, Qujing 655011, P. R. China

E-mail Address: nadeem@mail.qjnu.edu.cn

Corresponding author.

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and

ZITIAN LI

School of Mathematics and Statistics, Qujing Normal University, Qujing 655011, P. R. China

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https://doi.org/10.1142/S0218348X23500688Cited by:1 (Source: Crossref)

Abstract

This study presents the modified form of the homotopy perturbation method (HPM), and the Yang transform is adopted to simplify the solving process for the Kuramoto–Sivashinsky (KS) problem with fractal derivatives. This scheme is established by combining the two-scale fractal scheme and Yang transform, which is very helpful to evaluate the approximate solution of the fractal KS problem. Initially, we transfer the fractal problem into its partners using the two-scale fractal approach, and then we use the Yang transform ( $𝒴$ T) to obtain the recurrent relation. Second, the HPM is then introduced to deal with the nonlinear elements of the fractal model. The numerical example demonstrates how the suggested technique is incredibly straightforward and precise for nonlinear fractal models. In addition, the graphical error of the proposed fractal model is compared with the calculated results of our suggested approach and the exact results. This graphical error displays the strength and authenticity of our proposed scheme.

Keywords:

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