中文摘要：

研究分数微分的阶数对分数导数型Duffing振子动力学行为的影响，运用数值仿真模拟分数Duffing振子随分数微分阶数变化而变化的规律．数据表明，分数微分阶值的变化，会引起由分数微分算子描述的非线性振子动力学行为的显著变化．存在最优分数微分阶值，可以作为表达非线性振子复杂动力学行为如混沌振动发生可能性的一种判断指标．

英文摘要：

This paper presents the study of the influence of fractional differential orders upon the dynamic behavior of fractional Dulling-like oscillator. The numerical simulation is made to investigate into the problems concerned, the results show that the change of the values of fractional differential order can cause the substantial change of dynamic behavior of the nonlinear system modeled by fractional derivative operator, and the optimal fractional differential order exists for the nonlinear system described by fractional operator, which can be used as an indicator to identify the complicated dynamic behaviors like chaotic vibration.