Generalized differential transform method (GDTM) is a powerful method to solve the fractional differential equations.In this paper, a new fractional model Rollerball pen for systems with single degree of freedom (SDOF) is presented, by using the GDTM.The advantage of this method compared with some other numerical methods has been shown.The analysis of new approximations, damping and acceleration of systems are also described.Finally, by reducing damping and analysis of the errors, in one of the fractional cases, we have shown that in addition to having a suitable solution Training aids for the displacement close to the exact one, the system enjoys acceleration once crossing the equilibrium point.