About the Noether's theorem for fractional Lagrangian systems and a generalization of the classical Jost method of proof

DOI10.1515/fca-2019-0048zbMath1473.70038arXiv1802.01735OpenAlexW2982127716WikidataQ126987558 ScholiaQ126987558MaRDI QIDQ2175761

Anna Szafrańska, Jacky Cresson

Publication date: 30 April 2020

Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.01735

zbMATH Keywords

Euler-Lagrange equationssymmetriesfractional calculusNoether's theorem

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) Optimality conditions for free problems in one independent variable (49K05) Fractional ordinary differential equations (34A08)

Related Items (11)

Noether's theorem for fractional Birkhoffian system of Herglotz type with time delay ⋮ Continuous and discrete Noether's fractional conserved quantities for restricted calculus of variations ⋮ Fractional time-scales Noether theorem with Caputo \(\Delta\) derivatives for Hamiltonian systems ⋮ Local and global conserved quantities involving generalized operators ⋮ Noether’s theorem for Herglotz type variational problems utilizing complex fractional derivatives ⋮ Conservation laws for systems of non-standard Birkhoffians with fractional derivatives ⋮ Calculus of variations with higher order Caputo fractional derivatives ⋮ General fractional classical mechanics: action principle, Euler-Lagrange equations and Noether theorem ⋮ Noether’s-type theorems on time scales ⋮ Noether's theorem for variational problems of Herglotz type with real and complex order fractional derivatives ⋮ Caputo \(\Delta\)-type fractional time-scales Noether theorem of Birkhoffian systems

Cites Work

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• Variational problems with fractional derivatives: invariance conditions and Nöther's theorem
• Formulation of Euler-Lagrange equations for fractional variational problems
• A continuous/discrete fractional Noether's theorem
• Comments on various extensions of the Riemann-Liouville fractional derivatives: about the Leibniz and chain rule properties
• A counterexample to a Frederico-Torres fractional Noether-type theorem
• Noether's theorem on time scales
• Multiscale functions, scale dynamics, and applications to partial differential equations

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