Necessary and sufficient condition for a positive fractional linear continuous-time system to have its pseudo state bounded in a given interval is presented. Some previous results about fractional positive systems are completed. Generalization of an expression for the exponential function is obtained for the Mittag-Leffler function. Finally, necessary and sufficient condition is obtained for fractional positive systems to have their pseudo state bounded. An illustrative example is provided to show the usefulness of the results.