On a strong minimum condition of a fractal variational principle

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.

Automated summary

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.