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Noether theorem for non-conservative systems with time delay in phase space based on fractional model

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Abstract

In this paper, we focus on discussing the fractional Noether symmetries and fractional conserved quantities for non-conservative Hamilton system with time delay. Firstly, the fractional Hamilton canonical equations of non-conservative system with time delay are established; secondly, based upon the invariance of the fractional Hamilton action with time delay under the infinitesimal transformations of group, we obtain the definitions and criterion of fractional Noether symmetric transformations, fractional Noether quasi-symmetric transformations and fractional generalized Noether quasi-symmetric transformations in phase space; finally, the relationship between the fractional Noether symmetries and fractional conserved quantities with time delay in phase space is established. At the end of the paper, some examples are given to illustrate the application of the results.

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Acknowledgments

This project was supported by the National Natural Science Foundation of China (Grant Nos. 10972151 and 11272227).

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Authors and Affiliations

  1. School of Sciences, Nanjing University of Science and Technology, Nanjing, 210094, Jiangsu, People’s Republic of China

    Shi-Xin Jin

  2. College of Civil Engineering, Suzhou University of Science and Technology, Suzhou, 215011, Jiangsu, People’s Republic of China

    Yi Zhang

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  1. Shi-Xin Jin
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  2. Yi Zhang
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Correspondence to Yi Zhang.

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Jin, SX., Zhang, Y. Noether theorem for non-conservative systems with time delay in phase space based on fractional model. Nonlinear Dyn 82, 663–676 (2015). https://doi.org/10.1007/s11071-015-2185-z

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  • DOI: https://doi.org/10.1007/s11071-015-2185-z

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