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A NOVEL COMPUTATIONAL APPROACH TO THE LOCAL FRACTIONAL (3+1)-DIMENSIONAL MODIFIED ZAKHAROV–KUZNETSOV EQUATION

KANG-JIA WANG

https://orcid.org/0000-0002-3905-0844

School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, P. R. China

E-mail Address: konka05@163.com

Corresponding author.

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and

FENG SHI

https://orcid.org/0000-0002-1364-6148

School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, P. R. China

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https://doi.org/10.1142/S0218348X24500269Cited by:17 (Source: Crossref)

Abstract

The fractional derivatives have been widely applied in many fields and has attracted widespread attention. This paper extracts a new fractional (3+1)-dimensional modified Zakharov–Kuznetsov equation (MZKe) with the local fractional derivative (LFD) for the first time. Two special functions, namely, the ${LT}_{δ} (Ξ^{δ})$ and ${LC}_{δ} (Ξ^{δ})$ functions that are derived on the basis of the Mittag-Leffler function (MLF) defined on the Cantor set (CS), are employed to construct the auxiliary trial function to look into the exact solutions (ESs). Aided by Yang’s non-differentiable (ND) transformation, six groups of the ND ESs are found. The ND ESs on the CS for $δ = ln 2 / ln 3$ are depicted graphically. Additionally, as a comparison, the ESs of the classic (3+1)-dimensional MZKe for $δ = 1$ are also illustrated. The outcomes reveal that the derived method is powerful and effective, and can be used to deal with the other local fractional PDEs.

Keywords:

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