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.

Caputo fractional derivative; System of fractional differential equations; Adomian decomposition; Bagley–Torvik equation; Fractional oscillation equation; Mittag-Leffler function