English
Related papers

Related papers: A formulation of Noether's theorem for fractional …

200 papers

We obtain Euler-Lagrange equations, transversality conditions and a Noether-like theorem for Herglotz-type variational problems with Lagrangians depending on generalized fractional derivatives. As an application, we consider a damped…

Optimization and Control · Mathematics 2017-07-19 Roberto Garra , Giorgio S. Taverna , Delfim F. M. Torres

The theory of the calculus of variations for fuzzy systems was recently initiated in [7], with the proof of the fuzzy Euler-Lagrange equation. Using fuzzy Euler-Lagrange equation, we obtain here a Noether-like theorem for fuzzy variational…

Optimization and Control · Mathematics 2017-08-23 J. Soolaki , O. S. Fard , R. Almeida , A. H. Borzabadi

A didactic and systematic derivation of Noether point symmetries and conserved currents is put forward in special relativistic field theories, without a priori assumptions about the transformation laws. Given the Lagrangian density, the…

General Physics · Physics 2016-03-17 Fernando Haas

We extend the second Noether theorem to fractional variational problems which are invariant under infinitesimal transformations that depend upon $r$ arbitrary functions and their fractional derivatives in the sense of Caputo. Our main…

Optimization and Control · Mathematics 2012-03-13 Agnieszka B. Malinowska

English version of abstract: The dynamic optimization problems treated by the calculus of variations are usually solved with the help of the 2nd order Euler-Lagrange differential equations. These equations are, generally speaking,…

Optimization and Control · Mathematics 2011-09-02 Paulo D. F. Gouveia , Delfim F. M. Torres

In this paper, we derive sufficient conditions ensuring the existence of a weak solution $u$ for a tempered fractional Euler-Lagrange equations $$ \frac{\partial L}{\partial x}(u,{^C}\mathbb{D}_{a^+}^{\alpha, \sigma} u, t) +…

Analysis of PDEs · Mathematics 2023-12-12 César E. Torres Ledesma , Gastao F. Frederico , Manuel M. Bonilla , J. Ávalos Rodríguez

We give a version of Noether theorem adapted to the framework of mu-symmetries; this extends to such case recent work by Muriel, Romero and Olver in the framework of lambda-symmetries, and connects mu-symmetries of a Lagrangian to a…

Mathematical Physics · Physics 2009-11-13 G. Cicogna , G. Gaeta

In this work we prove a weak Noether type theorem for a class of variational problems which include broken extremals. We then use this result to prove discrete Noether type conservation laws for certain classes of finite element…

Numerical Analysis · Mathematics 2015-03-17 Elizabeth Mansfield , Tristan Pryer

Noether's First Theorem yields conservation laws for Lagrangians with a variational symmetry group. The explicit formulae for the laws are well known and the symmetry group is known to act on the linear space generated by the conservation…

Differential Geometry · Mathematics 2013-02-18 Tania M. N. Goncalves , Elizabeth L. Mansfield

Some problems on variations are raised for classical discrete mechanics and field theory and the difference variational approach with variable step-length is proposed motivated by Lee's approach to discrete mechanics and the difference…

High Energy Physics - Theory · Physics 2009-11-07 Han-Ying Guo , Ke Wu

A class of generalized Galileon cosmological models, which can be described by a point-like Lagrangian, is considered in order to utilize Noether's Theorem to determine conservation laws for the field equations. In the…

General Relativity and Quantum Cosmology · Physics 2017-03-23 N. Dimakis , Alex Giacomini , Sameerah Jamal , Genly Leon , Andronikos Paliathanasis

We derive the variational principle and Noether's theorem in generally covariant field theory in an explicitly coordinate-independent way by means of the exterior calculus over the space-time manifold. We then focus on the symmetry of…

General Relativity and Quantum Cosmology · Physics 2014-04-10 Ermis Mitsou

We extend Noether's symmetry theorem to the fractional Riemann-Liouville integral functionals of the calculus of variations recently introduced by El-Nabulsi.

Optimization and Control · Mathematics 2007-05-23 Gastao S. F. Frederico , Delfim F. M. Torres

Noether's Theorem is familiar to most physicists due its fundamental role in linking the existence of conservation laws to the underlying symmetries of a physical system. Typically the systems are described in the particle-based context of…

Statistical Mechanics · Physics 2022-05-04 Sophie Hermann , Matthias Schmidt

Noether's calculus of invariant variations yields exact identities from functional symmetries. The standard application to an action integral allows to identify conservation laws. Here we rather consider generating functionals, such as the…

Statistical Mechanics · Physics 2021-08-16 Sophie Hermann , Matthias Schmidt

Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of…

Optimization and Control · Mathematics 2017-04-14 Matheus J. Lazo , Delfim F. M. Torres

The connection between symmetries and conservation laws as made by Noether's theorem is extended to the context of causal variational principles and causal fermion systems. Different notions of continuous symmetries are introduced. It is…

Mathematical Physics · Physics 2016-05-13 Felix Finster , Johannes Kleiner

We present a general algorithm constructing a discretization of a classical field theory from a Lagrangian. We prove a new discrete Noether theorem relating symmetries to conservation laws and an energy conservation theorem not based on any…

Mathematical Physics · Physics 2023-09-14 Mikhail Skopenkov

We establish a new version of the first Noether Theorem, according to which the (equivalence classes of) first integrals of given Euler-Lagrange equations in one independent variable are in exact one-to-one correspondence with the…

Mathematical Physics · Physics 2015-06-23 Emanuele Fiorani , Andrea Spiro

An investigation of classical fields with fractional derivatives is presented using the fractional Hamiltonian formulation. The fractional Hamilton's equations are obtained for two classical field examples. The formulation presented and the…

General Physics · Physics 2011-07-11 A. A. Diab , R. S. Hijjawi , J. H. Asad , J. M. Khalifeh