FRACTIONAL MECHANICS - A NONCOMMUTATIVE APPROACH

The extension of coordinate space and of phase space with noncommutative algebra structure is proposed. For models on such a space the corresponding Euler-Lagrange equations are derived via minimum action principle. It appears that equations of motion in the noncommutative framework do not mix left and right derivatives thus being simple to solve at least in the linear case. Then the Hamiltonian and Hamilton's equations are discussed for general sequential model. The oscillator with friction depending linearly on velocity and the model of two interacting oscillators are studied as an application.