  In this paper, we present some results for existence of global solutions and
attractivity for mulidimensional fractional differential equations involving
Riemann-Liouville derivative. First, by using a Bielecki type norm and Banach
fixed point theorem, we prove a Picard-Lindel\"of type theorem on the existence
and uniqueness of solutions. Then, applying the properties of Mittag-Leffler
functions, we describe the attractivity of solutions to some classes of
Riemann--Liouville linear fractional differential systems.
