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Symmetries and conserved quantities for fractional action-like Pfaffian variational problems

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Abstract

The fractional Pfaffian variational problems and the fractional Noether theory are studied under a fractional model presented by El-Nabulsi. Firstly, the fractional action-like Pfaffian variational problem is presented, the El-Nabulsi–Pfaff–Birkhoff–d’Alembert fractional principle is established, then the El-Nabulsi–Birkhoff fractional equations are derived; secondly, the definitions and criteria of the fractional Noether symmetric transformations are given, which are based on the invariance of El-Nabulsi–Pfaffian action under the infinitesimal transformations of group, then the inner relationship between a fractional Noether symmetry and a fractional conserved quantity is established; finally, two examples are given to illustrate the application of the results.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (grant Nos. 10972151 and 11272227), the Innovation Program for Postgraduate in Higher Education Institutions of Jiangsu Province (No. CXZZ11_0949), and the Innovation Program for Postgraduate of Suzhou University of Science and Technology (No. SKCX11S_050).

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  1. College of Civil Engineering, Suzhou University of Science and Technology, Suzhou, 215009, P.R. China

    Yi Zhang

  2. College of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou, 215009, P.R. China

    Yan Zhou

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  1. Yi Zhang
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Correspondence to Yi Zhang.

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Zhang, Y., Zhou, Y. Symmetries and conserved quantities for fractional action-like Pfaffian variational problems. Nonlinear Dyn 73, 783–793 (2013). https://doi.org/10.1007/s11071-013-0831-x

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