A new method of fractional dynamics, i.e., fractional Mei symmetrical method for finding conserved quantity, and its applications to physics

DOI10.1007/s10773-016-3055-2zbMath1406.70025OpenAlexW2411607372MaRDI QIDQ517832

Yun Dai, Shao-Kai Luo, Jin-Man He, Xiao-Tian Zhang

Publication date: 28 March 2017

Published in: International Journal of Theoretical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10773-016-3055-2

zbMATH Keywords

conserved quantityfractional general relativistic Buchduhl modelfractional generalized Hamiltonian systemfractional Mei symmetryfractional Robbins-Lorenz modelfractional three-body model

Mathematics Subject Classification ID

Three-body problems (70F07) Hamilton's equations (70H05) Fractional derivatives and integrals (26A33) Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics (70H40) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33)

Related Items (10)

Basic theory of fractional Mei symmetrical perturbation and its applications ⋮ Basic theory of fractional conformal invariance of Mei symmetry and its applications to physics ⋮ On the families of fractional dynamical models ⋮ Conserved quantities of conservative continuous systems by Mei symmetries ⋮ Conformal invariance and conserved quantities of mechanical system with unilateral constraints ⋮ Adiabatic invariants for generalized fractional Birkhoffian mechanics and their applications ⋮ A new method of fractional dynamics, i.e., fractional generalized Hamilton method with additional terms, and its applications to physics ⋮ A new type of fractional Lie symmetrical method and its applications ⋮ Noether symmetry and conserved quantity for fractional Birkhoffian mechanics and its applications ⋮ Mei symmetry and conservation laws for time-scale nonshifted Hamilton equations

Cites Work

• Unnamed Item
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• Conformal invariance and Mei conserved quantity for generalized Hamilton systems with additional terms
• Conformal invariance of Mei symmetry and conserved quantities of Lagrange equation of thin elastic rod
• Fractional generalized Hamiltonian mechanics
• A Lie symmetrical basic integral variable relation and a new conservation law for generalized Hamiltonian systems
• Lie algebraic structure and generalized Poisson conservation law for fractional generalized Hamiltonian systems
• A new type of non-Noether exact invariants and adiabatic invariants of generalized Hamiltonian systems
• Generalized variational calculus in terms of multi-parameters fractional derivatives
• A new method of dynamical stability, i.e. fractional generalized Hamiltonian method, and its applications
• A new method of finding the fractional Euler-Lagrange and Hamilton equations within Caputo fractional derivatives
• Fractional Nambu dynamics
• On fractional Euler-Lagrange and Hamilton equations and the fractional generalization of total time derivative
• Fractional Hamiltonian formalism within Caputo's derivative
• Generalized variational problems and Euler-Lagrange equations
• Symmetries and conservation laws for generalized Hamiltonian systems
• Fractional relativistic Yamaleev oscillator model and its dynamical behaviors
• Fractional sequential mechanics - models with symmetric fractional derivative.
• Lagrangean and Hamiltonian fractional sequential mechanics.
• Form invariance and Noether symmetrical conserved quantity of relativistic Birkhoffian systems
• Conformal invariance of Mei symmetry for the non-holonomic systems of non-Chetaev's type
• On the fractional Hamilton and Lagrange mechanics
• Special Mei symmetry and approximate conserved quantity of Appell equations for a weakly nonholonomic system
• Conformal invariance and conserved quantity for the nonholonomic system of Chetaev's type
• Fractional dynamics of relativistic particle
• Perturbation to Mei symmetry and generalized Mei adiabatic invariants for Birkhoffian systems
• Fractional Lorentz-Dirac model and its dynamical behaviors
• Fractional Birkhoffian mechanics
• Contracted Hamiltonian on symmetric space \(SU(3)/SU(2)\) and conserved quantities
• Fractional generalized Hamiltonian equations and its integral invariants
• Fractional generalized Hamiltonian mechanics and Poisson conservation law in terms of combined Riesz derivatives
• Stability for manifolds of the equilibrium state of fractional Birkhoffian systems
• Stability for manifolds of equilibrium states of fractional generalized Hamiltonian systems
• Two Types of New Conserved Quantities and Mei Symmetry of Mechanical Systems in Phase Space
• Dynamical symmetries and conserved quantities
• Generalized classical dynamics, and the ‘classical analogue’ of a Fermioscillator
• Fractional embedding of differential operators and Lagrangian systems
• A direct approach to the construction of standard and non-standard Lagrangians for dissipative-like dynamical systems with variable coefficients
• On the complete integrability and linearization of certain second-order nonlinear ordinary differential equations
• On the hamiltonian structure of non-local field theories

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