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New Exact Solutions Of The Local Fractional Modified Equal Width-Burgers Equation On The Cantor Sets

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  • KANG-JIA WANG

    (School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo, 454003, P. R. China)

Abstract

This study proposes a new fractal modified equal width-Burgers equation (MEWBE) with the local fractional derivative (LFD) for the first time. By defining the Mittag-Leffler function (MLF) on the Cantor set (CS), two special functions, namely, the THυ(μυ) and CHυ(μυ) functions, are derived for constructing the auxiliary function to seek the non-differentiable (ND) exact solutions. And 16 groups of the ND exact solutions are successfully established. The solutions on the CS are depicted graphically to interpret the nonlinear dynamic behaviors. Furthermore, the comparative results of the fractal MEWBE and the classical MEWBE are also discussed. The obtained results confirm that the proposed method is effective and powerful, and can provide a promising way to find the ND exact solutions of the local fractional PDEs.

Suggested Citation

  • Kang-Jia Wang, 2023. "New Exact Solutions Of The Local Fractional Modified Equal Width-Burgers Equation On The Cantor Sets," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(09), pages 1-9.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:09:n:s0218348x23501116
    DOI: 10.1142/S0218348X23501116
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    Cited by:

    1. Khater, Mostafa M.A., 2024. "Dynamic insights into nonlinear evolution: Analytical exploration of a modified width-Burgers equation," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).

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