发表机构
School of Engineering and Sciences, Tecnológico de Monterrey; Physics Department, Cinvestav（蒙特雷理工学院科学与工程学部; 墨西哥国立科学研究与高级研究中心物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对含显式分数阶阻尼的三参数分数阶微分方程，分析外力驱动下分数阶振荡器的响应，明确外力决定其长期行为，给出不同外力下的精确解特征。
AI 中文摘要
我们研究了当动力学定律包含显式分数阶阻尼项时，分数阶振荡器对外力的响应。对应的三参数分数阶微分方程（Caputo型）存在精确解。其中两个分数参数与产生连续能量耗散的本征耗散机制相关，第三个分数参数表征阻尼项，振荡器受外力驱动对抗该阻尼项。当包含随时间变化的外力时，该分数阶动力学定律与粘弹性材料的Newton-Scott-Blair模型相关。外力的拉普拉斯变换决定解的形式，具体例子包括无外力、恒力、正弦力和阶跃外力。在恒力驱动下，系统在瞬态阶段后达到固定位置；在正弦力驱动下，系统呈现持续振荡行为。这些结果表明，外力决定了带分数阻尼的振荡器的长期行为。
英文摘要
We investigate how a fractional oscillator reacts to external forces when the dynamic law includes a damping term that is explicitly fractional. The corresponding three-parametric fractional differential equation (in the Caputo sense) admits exact solution. Two of the fractional parameters are associated with the intrinsic dissipation mechanism that produces continuous dissipation of energy. The third fractional parameter characterizes the damping term against which the oscillator is driven by the external force. When external time-dependent forces are included, the fractional dynamic law is associated with the Newton-Scott-Blair model of viscoelastic materials. The Laplace transform of the external force defines the profile of the solution; specific examples include the absence of external forces as well as constant, sinusoidal and stepped external forces. With a constant driving force, the system reaches a fixed position after a transient period. With a sinusoidal driving force, the system exhibits persistent oscillatory behavior. These results suggest that the external driving force determines the long-term behavior of the fractionally damped oscillator.
CommentsLaTex file, 27 pages, 7 figures
