STUDY ON THE LOCAL FRACTIONAL (3+1)-DIMENSIONAL MODIFIED ZAKHAROV–KUZNETSOV EQUATION BY A SIMPLE APPROACH

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

FRACTALS (fractals), 2024, vol. 32, issue 05, 1-11

Abstract: Under the current research, the local fractional (3+1)-dimensional modified Zakharov–Kuznetsov equation (MZKE) is explored. With the Mittag–Leffler function (MLF) defined on the Cantor sets (CS), four special functions, namely the SHχ(ℑχ), CHχ(ℑχ), SEχ(ℑχ) and CSχ(ℑχ) are extracted to construct an auxiliary function. Then the auxiliary function, along with Yang’s non-differentiable (ND) transformation, is manipulated to explore the ND exact solutions (ESs). By means of the proposed method, four different sets of the ND ESs are found in just one step. The nonlinear dynamics of the ND exact solutions on the CS are illustrated graphically. Furthermore, the ND exact solutions for χ =ln 2/ln3 and the classic exact solutions for χ = 1 are also compared and discussed in detail via the 2-D curves. The attained results reveal that the method is a simple but effective tool to deal with local fractional PDEs arising in physics and maths.

Keywords: Local Fractional Derivative; Local Fractional (3+1)-Dimensional Modified Zakharov–Kuznetsov Equation; Mittag–Leffler Function; Special Functions; Auxiliary Function (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24500919

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