In this paper, we discuss few existence result for solution of an infnite system of fractional differential equations of order α (1 < α < 2), with three point boundary value problem in the interval [0, T]. The problem is studied in the classical Banach sequence spaces c 0 and p (1 ≤ p < ∞), using Hausdorff measure of noncompactness and Darbo type fixed point theorem. We also illustrate our results through some concrete examples..