NEW EXACT SOLUTIONS OF THE LOCAL FRACTIONAL MODIFIED EQUAL WIDTH-BURGERS EQUATION ON THE CANTOR SETS

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

FRACTALS (fractals), 2023, vol. 31, issue 09, 1-9

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.

Keywords: Local Fractional Derivative; Cantor Set; Special Functions; Auxiliary Functions; Fractal Modified Equal Width-Burgers Equation (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23501116

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