Using the recent formulation of Noether’s theorem for the problems of the calculus of variations with fractional derivatives, the Lagrange multiplier technique, and the fractional Euler-Lagrange equations, we prove a Noetherlike theorem to the more general context of the fractional optimal control. As a corollary, it follows that in the fractional case the autonomous Hamiltonian does not define...

During each ovarian cycle, only a definite number of follicles ovulate, while the others undergo a degeneration process called atresia. We have designed a multi-scale mathematical model where ovulation and atresia result from a hormonal controlled selection process. A 2D-conservation law describes the age and maturity structuration of the follicular cell population. In this paper, we focus on t...

A complete conservation law classification is given for nonlinear telegraph (NLT) systems with respect to multipliers that are functions of independent and dependent variables. It turns out that a very large class of NLT systems admits four nontrivial local conservation laws. The results of this work are summarized in tables which display all multipliers, fluxes and densities for the correspond...

A simple conservation law formula for field equations with a scaling symmetry is presented. The formula uses adjoint-symmetries of the given field equation and directly generates all local conservation laws for any conserved quantities having non-zero scaling weight. Applications to several soliton equations, fluid flow and nonlinear wave equations, Yang-Mills equations and the Einstein gravita...

this paper introduces a mesh generating algorithm for solving the traffic flow equation as a conservation law equation. the idea behind the new method is to use the characteristic curves and moving non-oscillatory finite volume method. in addition, when characteristic curves intersect, the proposed scheme uses shock speed equation in order to improve computational efficiency. we also compare...

in this paper, heir-equations method is applied to investigate nonclassical symmetries and new solutions of the black-scholes equation. nonlinear self-adjointness is proved and infinite number of conservation laws are computed by a new conservation laws theorem.

In a matching paper [16], I proved that Conservation of Size and Information in a discrete token based system is overwhelmingly likely to lead to a power-law component size distribution with respect to the size of its unique alphabet. This was substantiated to a very high level of significance using some 55 million lines of source code of mixed provenance. The principle was also applied to show...

An open question in numerical analysis of multidimensional scalar conservation laws discretized on non-structured grids is the optimal rate of convergence. The main difficulty relies on a priori BV bounds which cannot be derived by opposition to the case of structured (cartesian) grids. In this paper we consider a related question for a corresponding continuous model, namely the vanishing visco...

In the present work a number of questions concerning foundations of the classical electrodynamics is discussed. First of all they are the law of the energy conservation and the introduction of particles in the classical electrodynamics. We pay attention to a logic error which takes place at an interpretation of the Poynting's theorem following from the equations of Maxwell-Lorentz as the law of...

We consider finite volume relaxation schemes for multidimensional scalar conservation laws. These schemes are constructed by appropriate discretization of a relaxation system and it is shown to converge to the entropy solution of the conservation law with a rate of h1/4 in L∞([0, T ], Lloc(R d)) .