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.