This article deals with the solution of a fractionally-damped generalized Bagley–Torvik (BT) equation whose damping characteristics are well-defined by means of the fractional derivative (FD) of the Riemann–Liouville and the Liouville–Caputo types. The Ho-motopy Analysis Method (HAM) is implemented for computing the dynamic response (DR) analysis. Two external forces or loads (namely, the unit step function and the unit impulse function) are considered for the analysis presented here. The FD is first defined and then used here in the Riemann–Liouville sense and the Liouville–Caputo sense. In order to show the efficiency, powerfulness, and validations of the present analysis, the obtained results are compared with the solutions derived earlier by Suarez and Shokooh (1997) who used the eigenfunction expansion method and by Podlubny (1999) who used fractional-order Green’s function.

中文翻译：

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外部载荷作用下分数阻尼广义Bagley-Torvik方程的动力响应分析

本文讨论分数阻尼广义Bagley-Torvik（BT）方程的解，该方程的阻尼特性通过Riemann-Liouville和Liouville-Caputo类型的分数导数（FD）很好地定义。Ho-motopy分析方法（HAM）用于计算动态响应（DR）分析。这里介绍的分析考虑了两个外力或负载（即单位阶跃函数和单位脉冲函数）。FD首先定义，然后在黎曼-利维尔（Liieville-Liouville）感和利维尔-卡普托（Liouville-Caputo）感中使用。为了显示本分析的效率，功能和验证，