Noether Theorem for Fractional Singular Systems
Noether Theorem for Fractional Singular Systems
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DOI：
10.1051/wujns/2023283207
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发表时间：
2023-06
影响因子：
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通讯作者：
Chuanjing Song;X. Zhai
中科院分区：
文献类型：
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作者：
Chuanjing Song;X. Zhai
讨论了两个分数次广义系统的Noether定理。一个系统涉及混合整数和卡普托分数导数，另一个系统仅涉及卡普托分数导数。首先，给出了分数阶主约束和分数阶约束哈密顿方程。然后，建立了这两类分数次广义系统的分数次Noether定理，包括分数次Noether恒等式、分数次Noether拟恒等式和分数次守恒量。最后，通过两个算例说明了所得到的结果。
Noether theorems for two fractional singular systems are discussed. One system involves mixed integer and Caputo fractional derivatives, and the other involves only Caputo fractional derivatives. Firstly, the fractional primary constraints and the fractional constrained Hamilton equations are given. Then, the fractional Noether theorems of the two fractional singular systems are established, including the fractional Noether identities, the fractional Noether quasi-identities and the fractional conserved quantities. Finally, the results obtained are illustrated by two examples.