<p>This paper deals with the gradient stability and the gradient stabilizability of Caputo time fractional diffusion linear systems. First, we give sufficient conditions that allow the gradient Mittag-Leffler and strong stability, where we use a direct method based essentially on the spectral properties of the system dynamic. Moreover, we consider a class of linear and distributed feedback controls that Mittag-Leffler and strongly stabilize the state gradient. The proposed results lead to an algorithm that allows us to gradient stabilize the state of the fractional systems under consideration. Finally, we illustrate the effectiveness of the developed algorithm by a numerical example and simulations.</p>