Summary: Adomian’s decomposition method is employed to obtain solutions of a system of fractional differential equations. The convergence of the method is discussed with some illustrative examples. In particular, for the initial value problem
where is a real square matrix, the solution turns out to be
where denotes the multivariate Mittag-Leffler function defined for matrix arguments and is the matrix having th row as , and all other entries are zero. Fractional oscillation and Bagley-Torvik equations are solved as illustrative examples.