Abstract: Using the  fixed point theorem of cone expansion and cone compression, we investigated threepoint boundary value problem for a class   of RiemannLiouville fractional differential equation with two disturbance parameters. We established and proved the  existence theorem and nonexistence theorem of positive solutions of the problem. The results show the  parameters affect the existence of positive solutions.

Key words: L¹-Carathéodory condition, fixed point theorem, disturbance parameter, Riemann-Liouville fractional derivative, positive solution