VARIATIONAL PRINCIPLE AND APPROXIMATE SOLUTION FOR THE FRACTAL GENERALIZED BENJAMIN–BONA–MAHONY–BURGERS EQUATION IN FLUID MECHANICS

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

FRACTALS (fractals), 2021, vol. 29, issue 03, 1-8

Abstract: The well-known generalized Benjamin–Bona–Mahony–Burgers (gBBMB) equation is widely used in the fluid mechanics, but it becomes invalid under the non-smooth boundary. So this paper, for the first time ever, extends the gBBMB equation into the fractal form that still works under the non-smooth boundary. By using the semi-inverse method, we develop the fractal variational formulations for the problem, which can provide the conservation laws in an energy form, and reveal the possible solution structures of the equation. Furthermore, the two-scale transform method combined with the variational iteration method is used to solve the fractal gBBMB equation. The obtained results show a good agreement with the existed results.

Keywords: Variational Principle; Fractal Derivative; Two-scale Transform; Variational Iteration Method; Fractal Generalized Benjamin–Bona–Mahony–Burgers Equation; Semi-inverse Method (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21500754

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