In this paper, we consider a diffusion equation with fractional-time derivative with non-singular Mittag-Leffler kernel in Hilbert spaces. Existence and uniqueness of solution are proved by means of a spectral argument. The existence of solution is obtained for all values of the fractional parameter α ∈ (0, 1). Moreover, by applying control theory to the fractional diffusion problem we obtain an optimality system which has also a unique solution.