相关论文: Fractional conservation laws in optimal control th…

This paper is concerned with analyzing a class of fractional calculus of variations problems and their associated Euler-Lagrange (fractional differential) equations. Unlike the existing fractional calculus of variations which is based on…

A new form of governing equations is derived from Hamilton's principle of least action for a constrained Lagrangian, depending on conserved quantities and their derivatives with respect to the time-space. This form yields conservation laws…

We study differential systems for which it is possible to establish a correspondence between symmetries and conservation laws based on Noether identity: quasi-Noether systems. We analyze Noether identity and show that it leads to the same…

The nonlinear partial differential equations describing the spin dynamics of Heisenberg ferro and antiferromagnet are studied by Lie transformation group method. The generators of the admitted variational Lie symmetry groups are derived and…

A version of Noether's second theorem using Lagrange multipliers is used to investigate fluid relabelling symmetries conservation laws in magnetohydrodynamics (MHD). We obtain a new generalized potential vorticity type conservation equation…

This paper deals with conservation laws for mechanical systems with nonholonomic constraints. It uses a Lagrangian formulation of nonholonomic systems and a Cartan form approach. We present what we believe to be the most general relations…

Invariance theorems in analytical mechanics, such as Noether's theorem, can be adapted to continuum mechanics. For this purpose, it is useful to give a functional representation of the motion and to interpret the groups of invariance with…

We extend the DuBois-Reymond necessary optimality condition and Noether's symmetry theorem to the scale relativity theory setting. Both Lagrangian and Hamiltonian versions of Noether's theorem are proved, covering problems of the calculus…

We use the Lagrange-Noether methods to derive the conservation laws for models in which matter interacts nonminimally with the gravitational field. The nonminimal coupling function can depend arbitrarily on the gravitational field strength.…

In this article, we establish the Freidlin-Wentzell type large deviation principle and central limit theorem for stochastic fractional conservation laws with small multiplicative noise in kinetic formulation framework. The weak convergence…

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…

The invariance theorems obtained in analytical mechanics and derived from Noether's theorems can be adapted to fluid mechanics. For this purpose, it is useful to give a functional representation of the fluid motion and to interpret the…

As is well known, there are different Lagrangians which lead to the same Euler-Lagrange operator. The gauge invariance of a Lagrangian guarantees that of the corresponding Euler-Lagrange operator, but not vice versa. We show that the gauge…

Fractional variation is defined as the limit of the difference quotient of the increments of a function and its argument raised to a fractional power. Fractional velocity can be suitable for characterizing singular behavior of derivatives…

The first part of this paper introduces sufficient conditions to determine conservation laws of diffusion equations of arbitrary fractional order in time. Numerical methods that satisfy a discrete analogue of these conditions have…

A didatic approach of the Noether's theorem in classical mechanics is derived and used to obtain the laws of conservation.

Fractional kinetic theory plays a vital role in describing anomalous diffusion in terms of complex dynamics generating semi-Markovian processes. Recently, the variational principle and associated Levy Ansatz have been proposed in order to…

In this paper we study the infinitesimal symmetries, Newtonoid vector fields, infinitesimal Noether symmetries and conservation laws of Hamiltonian systems. Using the dynamical covariant derivative and Jacobi endomorphism on the cotangent…

This paper develops methods for simplifying systems of partial differential equations that have families of conservation laws which depend on functions of the independent or dependent variables. In some cases, such methods can be combined…

Noether's theorem in the realm of point dynamics establishes the correlation of a constant of motion of a Hamilton-Lagrange system with a particular symmetry transformation that preserves the form of the action functional. Although usually…