Linli Wang1, Yuheng Xiong1, Chunjian Xue2This email address is being protected from spambots. You need JavaScript enabled to view it., Jingli Fu3, and Zuoxu Wang4This email address is being protected from spambots. You need JavaScript enabled to view it.
1School of Mathematics and Statistics, Xinxiang University, Xinxiang 453000 China
2School of mechanical and electrical engineering, Xinxiang University, Xinxiang 453000 China
3Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018 China
4Zachry Department of Civil and Environmental Engineering, Texas A&M University, College Station TX77840 USA
Received: August 18, 2025 Accepted: October 15, 2025 Publication Date: November 12, 2025
Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.
This paper develops afractional factor to generalize Lie symmetry analysis to time-delayed fractional mechanical systems. Firstly, the fractional Hamilton’s principle are formulated incorporating non-potential forces and delayed coordinates. Moreover, applying the fractional variational principle, we derive the canonical equations of Hamilton. Besides, a systematic investigation of Lie symmetry is conducted for fractional dynamical systems with time delays. Furthermore, the conserved quantities are obtained through symmetry analysis. Two mechanical examples demonstrate that these symmetries uncover fundamental dynamical properties of time delayed fractional mechanical systems. The results provide new theoretical tools for analyzing and controlling fractional engineering systems with memory effects.
Keywords: Lie symmetry; fractional mechanical system; time delay; conserved quantities
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