On a strong minimum condition of a fractal variational principle. (September 2021)

• Record Type: Journal Article
• Authors: He, Ji-Huan; Qie, Na; He, Chun-hui; Saeed, Tareq
• Is Part Of: Applied mathematics letters. Volume 119(2021)
• Publication Date: 2021-09
• Subjects: Fractal oscillator -- Two-scale fractal derivative -- Fractal Weierstrass theorem -- Mathematical pendulum; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2021.107199
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: 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.