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Conserved Quantity and Adiabatic Invariant for Hamiltonian System with Variable Order

School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, China
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Symmetry 2019, 11(10), 1270; https://doi.org/10.3390/sym11101270
Received: 26 August 2019 / Revised: 30 September 2019 / Accepted: 6 October 2019 / Published: 10 October 2019
Hamiltonian mechanics plays an important role in the development of nonlinear science. This paper aims for a fractional Hamiltonian system of variable order. Several issues are discussed, including differential equation of motion, Noether symmetry, and perturbation to Noether symmetry. As a result, fractional Hamiltonian mechanics of variable order are established, and conserved quantity and adiabatic invariant are presented. Two applications, fractional isotropic harmonic oscillator model of variable order and fractional Lotka biochemical oscillator model of variable order are given to illustrate the Methods and Results.
Keywords: Hamiltonian system; fractional derivative of variable order; Noether symmetry; conserved quantity; adiabatic invariant Hamiltonian system; fractional derivative of variable order; Noether symmetry; conserved quantity; adiabatic invariant
MDPI and ACS Style

Song, C.-J.; Cheng, Y. Conserved Quantity and Adiabatic Invariant for Hamiltonian System with Variable Order. Symmetry 2019, 11, 1270.

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