Abstract
In this paper, we study some properties of shifted Legendre Polynomials. Based on these polynomials, we develop some new operational matrices. These matrices are used to find approximate solution of fractional order differential equations (FDEs) under boundary conditions. The idea is then extended to coupled system of FDEs. Some test problems are solved to show the efficiency of the proposed method. It is worthy to mention here that the method is computer oriented. We use MatLab to carry out necessary calculation. All our results are displayed graphically. Where necessary, we use tables to demonstrate our analysis.