Stability for manifolds of the equilibrium state of fractional Birkhoffian systems

DOI10.1007/s00707-015-1307-5zbMath1325.70046OpenAlexW1988109299MaRDI QIDQ2516713

Jin-Man He, Shao-Kai Luo, Yan-Li Xu

Publication date: 4 August 2015

Published in: Acta Mechanica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00707-015-1307-5

Mathematics Subject Classification ID

Stability for nonlinear problems in mechanics (70K20) Fractional partial differential equations (35R11)

Related Items (12)

Approximate Birkhoffian formulations for nonconservative systems ⋮ Basic theory of fractional Mei symmetrical perturbation and its applications ⋮ Basic theory of fractional conformal invariance of Mei symmetry and its applications to physics ⋮ Fractional relativistic Yamaleev oscillator model and its dynamical behaviors ⋮ On the families of fractional dynamical models ⋮ Conformal invariance and conserved quantities of mechanical system with unilateral constraints ⋮ A new method of dynamical stability, i.e. fractional generalized Hamiltonian method, and its applications ⋮ A new method of fractional dynamics, i.e., fractional generalized Hamilton method with additional terms, and its applications to physics ⋮ A new method of fractional dynamics, i.e., fractional Mei symmetrical method for finding conserved quantity, and its applications to physics ⋮ A general method of fractional dynamics, i.e., fractional Jacobi last multiplier method, and its applications ⋮ Fractional Nambu dynamics ⋮ Quasi-matrix and quasi-inverse-matrix projective synchronization for delayed and disturbed fractional order neural network

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The effect of fractional order in variable structure control
• Equilibrium points and periodic orbits of higher-order autonomous generalized Birkhoff system
• Fractional generalized Hamiltonian mechanics
• Stability for manifolds of equilibrium states of generalized Hamiltonian systems
• Lie algebraic structure and generalized Poisson conservation law for fractional generalized Hamiltonian systems
• Lie symmetrical perturbation and a new type of non-Noether adiabatic invariants for disturbed generalized Birkhoffian systems
• Particle swarm optimization with fractional-order velocity
• Fractional control of heat diffusion systems
• Generalized variational problems and Euler-Lagrange equations
• Fractional dynamics. Applications of fractional calculus to dynamics of particles, fields and media
• Hamiltonian formulation of systems with linear velocities within Riemann-Liouville fractional derivatives
• Formulation of Euler-Lagrange equations for fractional variational problems
• Chaotic phenomena and fractional-order dynamics in the trajectory control of redundant manipulators
• Fractional sequential mechanics - models with symmetric fractional derivative.
• Fractional Birkhoffian mechanics
• A new Lie symmetrical method of finding a conserved quantity for a dynamical system in phase space
• Fractional generalized Hamiltonian equations and its integral invariants
• A fractional gradient representation of the Poincaré equations
• Fractional generalized Hamiltonian mechanics and Poisson conservation law in terms of combined Riesz derivatives
• Hamiltonian formulation and action principle for the Lorentz-Dirac system
• Hojman Exact Invariants and Adiabatic Invariants of Hamilton System
• Stabilität der Gleichgewichtslage in einem nicht‐holonomen System
• Fractional embedding of differential operators and Lagrangian systems
• Fractional Optimal Control in the Sense of Caputo and the Fractional Noether's Theorem
• First Integrals and Integral Invariants of Relativistic Birkhoffian Systems
• Symplectic Schemes for Birkhoffian System
• A Geometrical Approach to Hojman Theorem of a Rotational Relativistic Birkhoffian System
• Nonholonomic constraints with fractional derivatives
• On stability of motion of nonholonomic systems
• The action principle for a system of differential equations
• On the hamiltonian structure of non-local field theories
• Birkhoffian formulations of nonholonomic constrained systems

This page was built for publication: Stability for manifolds of the equilibrium state of fractional Birkhoffian systems