EXACT SOLUTIONS OF THE LOCAL FRACTIONAL KdV EQUATION WITH DUAL POWER LAW NONLINEARITY ON THE CANTOR SETS

Chuan Du, Jin-Fei Guo, Yi-Chen Bai, Chang Liu and Kang-Jia Wang ()
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Chuan Du: School of Mechanical and Electrical Engineering, Xinxiang University, Xinxiang 453003, P. R. China
Jin-Fei Guo: School of Mechanical and Electrical Engineering, Xinxiang University, Xinxiang 453003, P. R. China
Yi-Chen Bai: ��School of Information Science and Engineering, Harbin Institute of Technology, Weihai 264209, P. R. China
Chang Liu: ��School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, P. R. China
Kang-Jia Wang: ��School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, P. R. China

FRACTALS (fractals), 2025, vol. 33, issue 07, 1-8

Abstract: This paper derives a new fractional KdV equation with dual power law nonlinearity (DPLN) in the sense of the local fractional derivative. Aided by the non-differentiable (ND) traveling wave transformation, an effective tool, namely, the Mittag-Leffler function-based method (MLFBM) is utilized to develop the exact solutions. The attained exact solutions on the Cantor sets are unveiled graphically with the help of Matlab. When the fractional order 𠜀 = 1, the exact solutions on the Cantor sets become the exact solutions of the classic KdV equation with DPLN, and the corresponding performances are also presented through the 3D plots. The outcomes strongly confirm that the proposed method is a vigorous tool to explore the exact solutions of the local fractional partial differential equations.

Keywords: Local Fractional Equations; Cantor Sets; Local Fractional Derivative; Mittag-Leffler Function Based Method (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25500501

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