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

Kang-Jia Wang and Feng Shi
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Kang-Jia Wang: School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, P. R. China
Feng Shi: School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, P. R. China

FRACTALS (fractals), 2024, vol. 32, issue 01, 1-9

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 LTδ(Ξδ) and LCδ(Ξδ) 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/ln3 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: Local Fractional Derivative; Local Fractional (3+1)-Dimensional Modified Zakharov–Kuznetsov Equation; Mittag-Leffler Function; Special Functions (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24500269

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