The interaction between the fractional order parameter and the damping parameter can play a relevant role for introducing different dynamical behaviors in a physical system. Here, we study the Duffing oscillator with a fractional damping term. Our findings show that for certain values of the fractional order parameter, the damping parameter, and the forcing amplitude high oscillations amplitude can be induced. This phenomenon is due to the appearance of a resonance in the Duffing oscillator only when the damping term is fractional.

中文翻译：

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分数阻尼引起杜芬振荡器的谐振行为

分数阶参数和阻尼参数之间的相互作用可以在物理系统中引入不同的动力学行为方面发挥相关作用。在这里，我们研究具有分数阻尼项的杜芬振荡器。我们的研究结果表明，对于分数阶参数、阻尼参数和强迫振幅的某些值，可以引起高振荡振幅。这种现象是由于只有当阻尼项为分数时，杜芬振荡器才会出现共振。