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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Chuan Du & Jin-Fei Guo & Yi-Chen Bai & Chang Liu & Kang-Jia Wang, 2025. "EXACT SOLUTIONS OF THE LOCAL FRACTIONAL KdV EQUATION WITH DUAL POWER LAW NONLINEARITY ON THE CANTOR SETS," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(07), pages 1-8.
    • Handle: RePEc:wsi:fracta:v:33:y:2025:i:07:n:s0218348x25500501
    DOI: 10.1142/S0218348X25500501
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