Adomian decomposition: a tool for solving a system of fractional differential equations

Adomian decomposition method has been employed to obtain solutions of a system of fractional differential equations. Convergence of the method has been discussed with some illustrative examples. In particular, for the initial value problem: [Dα1y1,…,Dαnyn]t=A(y1,…,yn)t,yi(0)=ci,i=1,…,n, where A=[aij] is a real square matrix, the solution turns out to be y¯(x)=E(α1,…,αn),1(xα1A1,…,xαnAn)y¯(0), where E(α1,…,αn),1 denotes multivariate Mittag-Leffler function defined for matrix arguments and Ai is the matrix having ith row as [ai1…ain], and all other entries are zero. Fractional oscillation and Bagley-Torvik equations are solved as illustrative examples.