This paper investigates the possible adoption of a fractional order sliding surface for the robust control of perturbed integer-order LTI systems. It is proved that the standard approach used in Sliding Model Control (SMC) cannot be used and a substantial redesign of the control policy is needed. A novel control strategy is discussed, ensuring that the sliding manifold is hit at an infinite sequence of time instants becoming denser as time grows. Interesting asymptotic properties are derived relatively to the closed loop response in the presence of a wide class of disturbances. It is also proved that the chattering phenomenon may be remarkably alleviated. A careful simulation study is reported using an electromechanical system taken from the literature, which includes also a comparative analysis of performances with respect to standard SMC and second-order SMC. (C) 2014 Elsevier Ltd. All rights reserved.