Noether symmetries for fractional generalized Birkhoffian systems in terms of classical and combined Caputo derivatives

DOI10.1007/s00707-020-02690-yzbMath1440.70011OpenAlexW3026976069MaRDI QIDQ2194380

Ying Zhou, Yi Zhang

Publication date: 25 August 2020

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

Full work available at URL: https://doi.org/10.1007/s00707-020-02690-y

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 (6)

Noether’s theorem for Herglotz type variational problems utilizing complex fractional derivatives ⋮ Piecewise derivatives versus short memory concept: analysis and application ⋮ Conservation laws for systems of non-standard Birkhoffians with fractional derivatives ⋮ Noether's theorem for variational problems of Herglotz type with real and complex order fractional derivatives ⋮ A study on the fractal-fractional epidemic probability-based model of SARS-CoV-2 virus along with the Taylor operational matrix method for its Caputo version ⋮ Caputo \(\Delta\)-type fractional time-scales Noether theorem of Birkhoffian systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fractional variational approach with non-standard power-law degenerate Lagrangians and a generalized derivative operator
• Noether symmetries and conserved quantities for fractional Birkhoffian systems
• Noether theorem and its inverse for nonlinear dynamical systems with nonstandard Lagrangians
• Fractional generalized Hamiltonian mechanics
• Fractional isoperimetric Noether's theorem in the Riemann-Liouville sense
• The effect of fractional parameter on a perfect conducting elastic half-space in generalized magneto-thermoelasticity
• On numerical solution to fractional nonlinear oscillatory equations
• Fractional variational problems from extended exponentially fractional integral
• Fractional Noether's theorem in the Riesz-Caputo sense
• Fractional action-like variational problems in holonomic, non-holonomic and semi-holonomic constrained and dissipative dynamical systems
• Fractional variational calculus with classical and combined Caputo derivatives
• Generalized variational calculus in terms of multi-parameters fractional derivatives
• A new method of finding the fractional Euler-Lagrange and Hamilton equations within Caputo fractional derivatives
• Stochastic averaging of strongly nonlinear oscillators with small fractional derivative damping under combined harmonic and white noise excitations
• The Hamilton formalism with fractional derivatives
• Fractional Hamilton-Jacobi equation for the optimal control of nonrandom fractional dynamics with fractional cost function
• Fractional functional with two occurrences of integrals and asymptotic optimal change of drift in the Black-Scholes model
• Fractional dynamics. Applications of fractional calculus to dynamics of particles, fields and media
• A formulation of Noether's theorem for fractional problems of the calculus of variations
• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• Noether's theory in classical nonconservative mechanics
• The Noether's theory of Birkhoffian systems
• Lie symmetries and conserved quantities of constrained mechanical systems
• Formulation of Euler-Lagrange equations for fractional variational problems
• Fractional sequential mechanics - models with symmetric fractional derivative.
• Lagrangean and Hamiltonian fractional sequential mechanics.
• A continuous/discrete fractional Noether's theorem
• Lie symmetry analysis, explicit solutions and conservation laws for the space-time fractional nonlinear evolution equations
• Determination of periodic solutions for nonlinear oscillators with fractional powers by He's modified Lindstedt-Poincaré method
• Fractional generalized Hamiltonian equations and its integral invariants
• Symmetries and conserved quantities for fractional action-like Pfaffian variational problems
• Hamilton’s principle with variable order fractional derivatives
• The action principle for dissipative systems
• Dynamical symmetries and conserved quantities
• Fractional embedding of differential operators and Lagrangian systems
• Fractional Optimal Control in the Sense of Caputo and the Fractional Noether's Theorem
• MODIFICATIONS AT LARGE DISTANCES FROM FRACTIONAL AND FRACTAL ARGUMENTS
• Computational Methods in the Fractional Calculus of Variations
• Variational problems with fractional derivatives: Euler–Lagrange equations
• Fractional actionlike variational problems

This page was built for publication: Noether symmetries for fractional generalized Birkhoffian systems in terms of classical and combined Caputo derivatives