Conserved quantities and adiabatic invariants for fractional generalized Birkhoffian systems |
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| Affiliation: | 1. College of Science, Nanjing University of Science and Technology, Nanjing 210094, China;2. College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China;1. EFDA Close Support Unit, Boltzmannstr. 2, D-85748 Garching, Germany;2. Max Planck Institute for Plasma Physics, Boltzmannstr. 2, D-85748 Garching, Germany;3. Unità Tecnica Fusione ENEA, C. R. Frascati, via E. Fermi 45, 00044 Frascati (Roma), Italy;4. Department of Physics, University of Turin, Via P. Giuria 1, 10125 Turin, Italy;5. Laboratory for Plasma Physics, LPP-ERM/KMS, TEC & Belgian EUROfusion Consortium Partner, Brussels, Belgium;6. Karlsruhe Institute of Technology (KIT), Association EURATOM-KIT, Kaiserstrasse 12, 76131 Karlsruhe, Germany;7. CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France;8. CCFE, Culham Science Centre, Abingdon OX143DB, UK;9. Centre de Recherches en Physique des Plasmas, Ecole Polytechnique Fédérale de Lausanne (EPFL), Station 13, CH-1015 Lausanne, Switzerland;10. Department of Physics, Aristotle University of Thessaloniki, Greece;11. School of Electrical and Computer Engineering, National Technical University of Athens, Greece |
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| Abstract: | Based on Riemann-Liouville fractional derivatives, conserved quantities and adiabatic invariants for fractional generalized Birkhoffian systems are investigated. Firstly, fractional generalized Birkhoff equations are obtained by studying fractional generalized Pfaff-Birkhoff principle. Secondly, the definition of fractional generalized quasi-symmetry is given, the criteria of fractional generalized quasi-symmetry and the corresponding conserved quantity are achieved for fractional generalized Birkhoffian systems. Thirdly, perturbation to symmetry and adiabatic invariants for disturbed fractional generalized Birkhoffian systems are presented. Finally, an example is given to illustrate the results. |
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| Keywords: | Conserved quantity Adiabatic invariant Riemann-Liouville fractional derivative Generalized Birkhoffian system |
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