The paper is devoted to the study of operational matrix method for approximating solution for nonlinear coupled system fractional differential equations. The main aim of this paper is to approximate solution for the problem under two different types of boundary conditions, ‐point nonlocal boundary conditions and mixed derivative boundary conditions. We develop some new operational matrices. These matrices are used along with some previously derived results to convert the problem under consideration into a system of easily solvable matrix equations. The convergence of the developed scheme is studied analytically and is conformed by solving some test problems.