Noether's theorem for fractional Birkhoffian systems of variable order

DOI10.1007/s00707-016-1622-5zbMath1361.70022OpenAlexW2345828062MaRDI QIDQ332692

Bin Yan, Yi Zhang

Publication date: 9 November 2016

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

Full work available at URL: https://doi.org/10.1007/s00707-016-1622-5

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33)

Related Items (16)

Variational problem of Herglotz type for Birkhoffian system and its Noether's theorems ⋮ Variational problems with partial fractional derivative: optimal conditions and Noether's theorem ⋮ Basic theory of fractional Mei symmetrical perturbation and its applications ⋮ Basic theory of fractional conformal invariance of Mei symmetry and its applications to physics ⋮ Noether-type conserved quantities on time scales for Birkhoffian systems with delayed arguments ⋮ A new type of adiabatic invariants for disturbed Birkhoffian system of Herglotz type ⋮ Conservation laws for systems of non-standard Birkhoffians with fractional derivatives ⋮ Herglotz-type principle and first integrals for nonholonomic systems in phase space ⋮ Noether's theorems for dynamical systems of two kinds of non-standard Hamiltonians ⋮ Noether theory for Birkhoffian systems with nabla derivatives ⋮ Theory of generalized canonical transformations for Birkhoff systems ⋮ Noether symmetry and conserved quantity for Hamiltonian system of Herglotz type on time scales ⋮ Noether symmetry and conserved quantity for fractional Birkhoffian mechanics and its applications ⋮ Mei symmetry and new conserved quantities of time-scale Birkhoff's equations ⋮ Noether Symmetry and Conserved Quantities of Fractional Birkhoffian System in Terms of Herglotz Variational Problem ⋮ Caputo \(\Delta\)-type fractional time-scales Noether theorem of Birkhoffian systems

Cites Work

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• Numerical analysis of a new space-time variable fractional order advection-dispersion equation
• Noether symmetries and conserved quantities for fractional Birkhoffian systems
• On the stability and convergence of the time-fractional variable order telegraph equation
• Second-order approximations for variable order fractional derivatives: algorithms and applications
• Numerical techniques for the variable-order time fractional diffusion equation
• Noether symmetries for non-conservative Lagrange systems with time delay based on fractional model
• Variable-order fractional derivatives and their numerical approximations
• Nonlinear dynamics and control of a variable order oscillator with application to the van der Pol equation
• A formulation of Noether's theorem for fractional problems of the calculus of variations
• Variational problems with fractional derivatives: invariance conditions and Nöther's theorem
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• The Noether's theory of Birkhoffian systems
• Variable order and distributed order fractional operators
• Noether's theorem for fractional variational problem from El-Nabulsi extended exponentially fractional integral in phase space
• Constitutive Dynamic-Order Model for Nonlinear Contact Phenomena
• Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term
• Mechanics with variable-order differential operators
• Integration and differentiation to a variable fractional order

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