In this work, we investigate a Riemann-Liouville-type impulsive fractional integral boundary value problem. Using the fixed point index, we obtain two existence theorems on positive solutions under some conditions concerning the spectral radius of the relevant linear operator. Our method improves and generalizes some results in the literature.

In this paper, we studied a Hadamard-type fractional Riemann-Stieltjes integral boundary value problem. The existence of nontrivial solutions was obtained by using the fixed-point method when the nonlinearities can be superlinear, suberlinear, and have asymptotic linear growth. Our results improved and generalized some results of the existing literature.