The Super Twisting Control Algorithm (STA) constitutes a powerful and robust technique for control and observation problems. The structure of the STA allows inducing second-order sliding modes, such that the sliding variable and its derivative remain at zero after some finite time. However, the STA requires the strong differentiability of the sliding variable and the weak differentiability of disturbances. Thus, the sliding variable should become from an adequate design, ensuring its strong differentiability. Nonetheless, in the more general case of not necessarily integer-order differentiable disturbances, a typical case in electromechanical systems due to non-smooth effects, alternative control methods need to be considered. For that reason, this paper proposes a structural modification of the STA, allowing the integral of the discontinuous function to assume a fractional order to compensate not necessarily integer-order differentiable disturbances. An experimental assessment is conducted, and comparisons to other sliding mode based controllers are presented to demonstrate the reliability of the proposed method.