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Perturbation to Noether symmetry for fractional dynamic systems of variable order

  • C. J. Song
  • Y. ZhangEmail author
Original Paper
  • 24 Downloads

Abstract

Fractional dynamic system of variable order is one of the interesting topics to study. Perturbation to symmetry, which is closely related to its integrability, is worth to be well studied. In this paper, Perturbation to Noether symmetry and adiabatic invariant are investigated in terms of Riemann–Liouville fractional derivative of variable order for fractional generalized Birkhoffian system. Then under some special conditions and transformations, adiabatic invariants for the fractional Birkhoffian system, the fractional Hamiltonian system and the fractional Lagrangian system are discussed. It has been observed that some results obtained from special cases are new and others are consistent with the existing results, which reconfirm the credibility of proposed achievements. Finally, an example is given to illustrate the methods and results.

Keywords

Perturbation to Noether symmetry Adiabatic invariant Fractional derivative of variable order Fractional dynamic system 

PACS Nos.

11.25.Db 11.30.-j 

Notes

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 11802193, 11572212, 11272227), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No. 18KJB130005), the Science Research Foundation of Suzhou University of Science and Technology (No. 331812137) and Natural Science Foundation of Suzhou University of Science and Technology.

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Copyright information

© Indian Association for the Cultivation of Science 2019

Authors and Affiliations

  1. 1.School of Mathematics and PhysicsSuzhou University of Science and TechnologySuzhouPeople’s Republic of China
  2. 2.College of Civil EngineeringSuzhou University of Science and TechnologySuzhouPeople’s Republic of China

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