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中文摘要：
基于El-Nabulsi动力学模型，提出并研究了Birkhoff系统基于按指数律拓展的分数阶积分的变分问题的Noether对称性与守恒量。基于按指数律拓展的分数阶积分的El-Nabulsi-Pfaff-Birkhoff变分问题，建立起与之对应的El-Nabulsi-Birkhoff方程；基于El-Nabulsi-Pfaff作用量在无限小变换下的不变性，给出系统的Noether对称变换和Noether准对称变换的定义和判据。该研究建立Birkhoff系统基于按指数律拓展的分数阶积分的变分问题的Noether定理，揭示了该模型下系统的Noether对称性和守恒量之间的关系。文末举例说明结果的应用。
英文摘要：
Based on El-Nabulsi dynamical model,the Noether symmetries and the conserved quantities for the variational problem of Birkhoffian system from extended exponentially fractional integral are pres-ented and studied.Firstly,the El-Nabulsi-Pfaff-Birkhoff variational problem from extended exponentially fractional integral is presented,then the corresponding El-Nabulsi-Birkhoff equations are derived.Sec-ondly,the definitions and the criteria of the Noether symmetric transformations and the Noether quasi-symmetric transformations of the system are given,which are based on the invariance of El-Nabulsi-Pfaff action under the infinitesimal transformations of group.Finally,the Noether theorem for the variational problem of Birkhoffian system from extended exponentially fractional integral is established,which reveals the inner relationship between a Noether symmetry and a conserved quantity.An example is given to il-lustrate the application of the results.
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