Fractional Lorentz-Dirac Model and Its Dynamical Behaviors

Abstract

In the paper, we construct a new kind of fractional dynamical model, i.e. the fractional Lorentz-Dirac model, and explore dynamical behaviors of the model. We find that the fractional Lorentz-Dirac model possesses Lie algebraic structure and satisfies generalized Poisson conservation law, and then a series of Poisson conserved quantities of the model are given. Further, the relation between conserved quantity and integral invariant of the model is studied, and it is proved that, using the Poisson conserved quantities, we can construct a series of integral invariants of the model. Finally, the stability for the manifolds of equilibrium state of the fractional Lorentz-Dirac model is studied.