期刊
APPLIED MATHEMATICS LETTERS
卷 119, 期 -, 页码 -出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.aml.2021.107199
关键词
Fractal oscillator; Two-scale fractal derivative; Fractal Weierstrass theorem; Mathematical pendulum
资金
- Taif university, Taif, Saudi Arabia [TURSP-2020/16]
Variational theory is essential for numerical methods, with a minimum variational principle guaranteeing convergence. This paper proposes a fractal modification of the Weierstrass function for fractal variational principles, providing a strong minimum condition. The correctness of this condition is demonstrated using the Hamilton least-action principle for the Duffing oscillator in a fractal space.
Variational theory is the theoretical basis for various numerical methods. A minimum variational principle plays an important role in guaranteeing the convergence of the numerical algorithm, and the Weierstrass theorem is used to judge the minimum. This paper suggests a fractal modification of Weierstrass function for fractal variational principles, and a strong minimum condition is given. The Hamilton least-action principle for the Duffing oscillator in a fractal space is used as an example to show the correctness of the suggested strong minimum condition. (C) 2021 Elsevier Ltd. All rights reserved.
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