In this paper, a novel fractional-order recursive integral terminal sliding mode (FORITSM) control is proposed for nonlinear systems in the presence of external disturbances with unknown bounds. The proposed control approach provides an easy-to implement solution capable of zeroing the sliding variable in a finite-time (FnT) by adding a fractional-order command filter. Moreover, the reaching phase is eliminated, and FnT convergence of the system states is proved. The proposed technique has also a chattering alleviation property, which is beneficial for practical cases, as the control of quadrotor UAVs presented in the paper. Finally, a simulation case study on a quadrotor system is illustrated to show the effectiveness of the proposed FORITSM control, also with respect to classical methods.