This paper deals with the study of existence of multiple positive solutions to a type of nonlinear fractional differential equation D α ( y ) + p ( t ) f ( y ( t ) ) = 0 , t ∈ ( 0 , 1 ) , 1 < α ≤ 2 together with the boundary condition y ( 0 ) = 0 , y ′ ( 1 ) = 0 , where D α represents the α-th order Riemann-Liouville type differential operator. p( t) is a positive continuous function on [0,1], and f:[0 ,∞)→[0 ,∞) is a continuous function. We use Schauder’s fixed point theorem to obtain at least one positive solution as well as we use Avery-Peterson fixed point theorem to obtain at least three positive solutions. . AMS Subject Categories: 34B18, 26A33 and 34B15.