A NOVEL VARIATIONAL PERSPECTIVE TO FRACTAL WAVE EQUATIONS WITH VARIABLE COEFFICIENTS

Xue-Feng Han and Kang-Le Wang
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Xue-Feng Han: School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, P. R. China
Kang-Le Wang: School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-8

Abstract: This paper aims at establishing two different types of wave models with unsmooth boundaries by the fractal calculus, and their fractal variational principles are successfully designed by employing the fractal semi-inverse transform method. A new approximate technology is proposed to solve the two fractal models based on the variational principle and fractal two-scale transform method. Finally, two numerical examples show that the proposed method is efficient and accurate, which can be extended to solve different types of fractal models.

Keywords: Fractal Derivative; Fractal Variational Principle; Two-Scale Transform Method (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22500268

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