On Conservation Laws for Models in Discrete, Noncommutative and Fractional Differential Calculus

摘要

We present the general method of derivation the explicit form of conserved currents for equations built within the framework of discrete, noncommutative or fractional differential calculus. The procedure applies to linear models with variable coefficients including also nonlinear potential part. As an example an equation on quantum plane, nonlinear Toda lattice model and homogeneous equation of fractional diffusion in 1 + 1 dimensions are studied.