Related papers: Conservation laws for time-fractional subdiffusion…
We determine the Lie point symmetries of a Gardner type system and establish its nonlinear self-adjointness. We then construct conservation laws via Ibragimov's Theorem.
In this work we consider the problem on group classification and conservation laws of the general first order evolution equations. We obtain the subclasses of these general equations which are quasi-self-adjoint and self-adjoint. By using…
We examine the validity of the principle of mass conservation for solutions of some typical equations in the theory of nonlinear diffusion, including equations in standard differential form and also their fractional counterparts. In Part 1,…
This paper presents a formulation of Noether's theorem for fractional classical fields. We extend the variational formulations for fractional discrete systems to fractional field systems. By applying the variational principle to a…
The method of nonlinear self-adjointness is applied to the Kadomtsev-Petviashvili equation. The infinite set of conservation laws associated with the infinite algebra of Lie point symmetry of the KP equation is constructed.
Fractional variational approach has gained much attention in recent years. There are famous fractional derivatives such as Caputo derivative, Riesz derivative and Riemann-Liouville derivative. Several versions of fractional variational…
We review the Lagrangian formulation of Noether symmetries (as well as "generalized Noether symmetries") in the framework of Calculus of Variations in Jet Bundles, with a special attention to so-called "Natural Theories" and "Gauge-Natural…
We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be…
Solutions to a class of conservation laws with discontinuous flux are constructed relying on the Crandall-Liggett theory of nonlinear contractive semigroups~\cite{CL}. In particular, the paper studies the existence of backward Euler…
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,…
We prove a Noether type symmetry theorem to fractional problems of the calculus of variations with classical and Riemann-Liouville derivatives. As result, we obtain constants of motion (in the classical sense) that are valid along the mixed…
Symmetry- and conservation law-preserving finite difference discretizations are obtained for linear and nonlinear one-dimensional wave equations on five- and nine-point stencils, using the theory of Lie point symmetries of difference…
We review the formulation of a Lorentz-covariant bispinorial wave function and wave equation for a single photon on a flat background. We show the existence of a 10-dimensional set of conservation laws for this equation, and prove that 8 of…
A Lagrangian formulation with nonlocality is investigated in this paper. The nonlocality of the Lagrangian is introduced by a new nonlocal argument that is defined as a nonlocal residual satisfying the zero mean condition. The nonlocal…
We derive the Noether identities and the conservation laws for general gravitational models with arbitrarily interacting matter and gravitational fields. These conservation laws are used for the construction of the covariant equations of…
The backward problem for subdiffusion equation with the fractional Riemann-Liouville time-derivative of order ? 2 (0; 1) and an arbitrary positive self-adjoint operator A is considered. This problem is ill-posed in the sense of Hadamard due…
This paper presents recent work on connections between symmetries and conservation laws. After reviewing Noether's theorem and its limitations, we present the Direct Construction Method to show how to find directly the conservation laws for…
A variational principle for Lagrangian densities containing derivatives of real order is formulated and the invariance of this principle is studied in two characteristic cases. Necessary and sufficient conditions for an infinitesimal…
Fractional Dzherbashian-Nersesian operator is considered and three famous fractional order derivatives namely Riemann-Liouville, Caputo and Hilfer derivatives are shown to be special cases of the earlier one. The expression for Laplace…
In this note, a numerical method based on finite differences to solve a class of nonlinear advection-diffusion fractional differential equation is proposed. The fractional operator considered here is the fractional Riemann-Liouville…