Matrix Mittag-Leffler function and solution of multi-term fractional differential equations

Abstract

In this paper, we first derive the solution of fractional differential equation system expressed in matrix Mittag-Leffler function by using the Adomian decomposition method. Then we consider the initial value problem (IVP) for multi-term fractional differential equation. By introducing new unknown functions, we rewrite the IVP for multi-term fractional differential equation into the IVP for a fractional differential equation system. Thus the solution can be given in terms of matrix Mittag-Leffler functions. We demonstrate the method using four numerical examples and the results are simulated using MATHEMATICA 8.