In this paper we are interested in the differential inclusion 0 ∈ ¨ x(t) + b t ˙ x(t) + ∂F (x(t)) in a finite-dimensional Hilbert space H, where F is a sum of two convex, lower semi-continuous functions with one being differentiable with Lipschitz gradient. The motivation of this study is that the differential inclusion models an accelerated version of proximal gradient algorithm called FISTA. In particular we prove existence of a global solution for this inclusion. Furthermore we show that under the condition b > 3, the convergence rate of F (x(t)) towards the minimimum of F is of order of o t −2 and that the solution-trajectory converges to a minimizer of F. These results generalize the ones obtained in the differential setting (where F is differentiable) in [6].