On systems of linear fractional differential equations with constant coefficients

This paper deals with the study of linear systems of fractional differential equations such as the following system: 0096-3 doi:10 * Co E-m Y ða 1⁄4 AðxÞY þ BðxÞ; ð1Þ where Y ða is the Riemann–Liouville or the Caputo fractional derivative of order a (0 < a 5 1), and AðxÞ 1⁄4 a11ðxÞ a1nðxÞ . . . . . . . . . an1ðxÞ annðxÞ 0BBBBBB@ 1CCCCCCA; BðxÞ 1⁄4 b1ðxÞ . . . . . . . . . bnðxÞ 0BBBBBB@ 1CCCCCCA ð2Þ are matrices of known real functions. In a way analogous to the usual case, we show how a generalized matrix exponential function and certain fractional Green function, in connection with the Mittag–Leffler type functions, would allow us to obtain an explicit representation of the general solution to the system (1) when A is a constant matrix. 2006 Published by Elsevier Inc.