NON-DIFFERENTIABLE EXACT SOLUTIONS OF THE LOCAL FRACTIONAL ZAKHAROV–KUZNETSOV EQUATION ON THE CANTOR SETS

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

FRACTALS (fractals), 2023, vol. 31, issue 03, 1-11

Abstract: In this study, a new fractional Zakharov–Kuznetsov equation (ZKE) within the local fractional derivative (LFD) is derived. Yang’s non-differentiable (ND) traveling wave transform is introduced, then two novel techniques namely the Mittag-Leffler function-based method (MLFBM) and Yang’s special function method (Y-SFM) are adopted to seek for the ND exact solutions for the first time. With the aid of the Mathematica software, the dynamic behaviors of the different solutions on the Cantor sets are illustrated via the 3D plots by assigning the appropriate parameters. The attained results confirm that the mentioned methods are effective and straightforward, which can be used to study the ND exact solutions of the local fractional partial differential equations (PDEs).

Keywords: Local Fractional Derivative; Local Fractional Zakharov–Kuznetsov Equation; Mittag-Leffler Function-Based Method; Non-Differentiable Exact Solution; Yang’s Special Function Method (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23500287

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