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中文摘要：
El-Nabulsi在研究非保守系统的动力学建模时，提出了三种类分数阶变分方法，即：基于Riemann-Liouville分数阶积分的变分问题，基于按指数律拓展的分数阶积分的变分问题和基于按周期函数律拓展的分数阶积分的变分问题。将上述三种El-Nabulsi动力学模型拓展到Birkhoff系统，建立了El-Nabulsi-Pfaff变分问题，导出了El-Nabulsi-Pfaff-Birkhoff-d’Alembert原理和El-Nabulsi-Birkhoff方程。文末，举例说明结果的应用。
英文摘要：
Studying the dynamical modeling of a non-conservative system, El-Nabulsi has put forward three kinds of fractional variational approaches： the fractional variational approach based on the definition of the Rie-mann-Liouville fractional integral, the fractional variational approach based on exponentially extended fractional integral, and the fractional variational approach based on the fractional integral extended by periodic law. In this article, we have extended these El-Nabulsi dynamical models to a Birkhoffian system and established the corre-sponding El-Nabulsi-Pfaff variational problems. Besides, we have deduced the El-Nabulsi-Pfaff-Birkhoff-d＇Alembert principles and the El-Nabulsi-Birkhoff equations. Finally, the application of the results is illustrated.
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