We consider a new fractional-order (FO) chaotic system displaying an interesting behavior named stick-slip motion. It consists of a simple model of spring-mass placed over a constant velocity v rolling  plate. The effect of small variations of the damping parameters and fractional derivatives on the dynamics of the mass is investigated both analytically and numerically. It turns out that the types of motions are significantly modified, particularly, in the case where fractional-order varies. Besides, it is verified that the shape of fixed point does not change, but only the position around which the oscillations take place linearly varies. The bifurcation diagram and the Lyapunov exponent of the FO system confirm that chaotic motion is converted into regular motion when fractional-order a decreases. It is also demonstrated that the state of fixed point is obtained from the intermittent motion by taking into account the fractional derivatives.

stick-slip motion, damping parameters, fractional-order derivation.