Abstract: By using the fixed point theorem and contraction mapping principle on a  cone in a real Banach space, the existence and uniqueness of positive solutions of nonlinear fractional differential equations in which the inhomogeneous term depends on the fractional derivative of lower orders were investigated respectively. Based on the expression of the solutions for this type equation, sufficient conditions for the existence of positive solutions for this type equation were obtained, also for the uniqueness. Meanwhile two examples were presented to demonstrate the main results.

Key words:  fractional differential equations, Caputo derivative, positive solution