The contribution of this paper is the design of a novel controller that enforces predefined-time convergence in fractional-order systems, which are defined by means of the Caputo derivative, whose order lays between zero and one. The controller is based on a dynamic extension, which induces an integer-order reaching phase, such that, the solution of the closed-loop system turns out to converge to the origin before a predefined fixed-time. The resulting controller is continuous and still able to face a large class of continuous but not necessarily differentiable disturbances. It is worth to remark that, the proposed controller does not include any term that depends on the initial conditions of the system, and that it is well-defined for any time. Numerical tests show the reliability of the proposed scheme.