## 1 Introduction  
Recently, the design of fractional order controllers has become one of the most exciting topics in control theory leading to interesting applications in the control of physical systems such as suspension systems, permanent magnet synchronous motors, power electronic systems and unmanned aerial vehicles, among others. The idea of fractional order control was first proposed by [1] introducing a robust fractional order control scheme. Also [PERSON] [2, 3] introduced the well known fractional order proportional-integral-derivative controller. Then, many fractional order controllers have been proposed in the literature, including tilt integral derivative (TID) controllers [4], fractional order lead-lag compensators [5, 6], fractional order optimal controllers [7, 8], and fractional order adaptive controllers [9, 10].  
On the other hand sliding mode control (SMC) is a well known control technique that is applied to both linear and nonlinear systems allowing to deal with uncertainties [11]. However, the monotonous switching feedback produced by these controllers causes high frequency chattering in the control signals, which leads to undesirable loads on control actuators [12, 13]. In recent years, fractional order sliding mode control (FOSMC) has been employed to overcome these drawbacks. For example, in [14], a control strategy called fractional order terminal sliding mode control (FOFSMC) is designed for a class of uncertain dynamical systems; a fractional order switching surface is proposed to satisfy a sliding condition and numerical simulations are provided that show the finite time stability of the closed-loopsystem. Also, in [15] a FOSMC is proposed for the control of a single-link flexible manipulator constructing a switching surface based on fractional derivatives; such a controller achieves better performance with small control chattering and robustness with respect to external load disturbances and parameter variations. A FOSMC for antilock braking systems (ABS) is proposed in [16; 17] to regulate the slip to a desired value; these controllers deal with the uncertainties in the ABS and track the desired slip faster than conventional integer order sliding mode control (IOSMC). Additionally, FOSMC has been used for speed control of permanent magnet synchronous motors [18], for vibration suppression of uncertain structures [19], for control of fractional order chaotic systems [20; 21] and so on leading to better control performance.  
In [22], the stability of a FOSMC has been studied showing that a stable reaching law, in the fractional order case, corresponds to a stable reaching law, in the integer order case. Also, a sufficient condition is derived to guarantee global attraction to the sliding surface when a fractional order linear system with uncertainties is considered. Motivated by this result, in this paper FOSMC design is proposed to solve a trajectory tracking problem for an integer order nonlinear system where an unknown additive perturbation term is present. A sufficient condition is also given that assures the reaching of a suitable sliding surface; on this surface trajectory tracking is performed. The FOSMC proposed is applied to the trajectory tracking problem of a quadrotor. For vertical take-off, trajectory tracking and landing, an error sliding surface is considered. Numerical simulations show the robustness of the FOSMC with respect to additive uncertainties (the error tracking is bounded to a small region around zero) and the chattering in the control signals is reduced when compared to a integer order sliding mode controller.  
The paper is organized as follows. In Section 2, fractional order differentiation is briefly presented together with the FOSMC proposed and the sufficient condition for the attractiveness of the sliding surface. Section 3 presents the FOSMC design for the trajectory control of a quadrotor model. Some simulations results are given in Section 4. Finally, in Section 5 some conclusions are presented.