Positive solutions of nonlocal fractional boundary value problem involving Riemann–Stieltjes integral condition

In this paper, we investigate the existence of positive solutions for a nonlocal fractional boundary value problem involving Caputo fractional derivative and nonlocal Riemann–Stieltjes integral boundary condition. By using the spectral analysis of the relevant linear operator and Gelfand’s formula, we obtain an useful upper and lower bounds for the spectral radius. Our discussion is based on the properties of the Green’s function and the fixed point index theory in cones.