In this paper we introduce the linear operator of fractional integral equation of the second kind (FIESK) in the framework of the Riemann-Liouville fractional calculus. Some results concerning the existence and uniqueness have been also obtained. Particular attention is devoted to the technique of Laplace transform for treating FIESK. By applying this technique we shall derive the analytical solutions of the most linear FIESK.Other main objective concern here is to give an approximate scheme using collocation method to solve FIESK. Two fundamental questions concerning this method: its stability and convergence are discussed. We show that the analytical stability bounds are in excellent agreement with numerical tests. Comparison between exact solutions and approximate predictions is made.