A generalization of the Mittag–Leffler function and solution of system of fractional differential equations

The solutions of system of linear fractional differential equations of incommensurate orders are considered and analytic expressions for the solutions are given by using the Laplace transform and multi-variable Mittag–Leffler functions of matrix arguments. We verify the result with numeric solutions of an example. The results show that the Mittag–Leffler functions are important tools for analysis of a fractional system. The analytic solutions obtained are easy to program and are approximated by symbolic computation software such as MATHEMATICA.