Existence of solutions for a higher order Riemann–Liouville fractional differential equation by Mawhin's coincidence degree theory

In this paper, we investigate the existence of at least one solution to the following higher order Riemann–Liouville fractional differential equation with Riemann–Stieltjes integral boundary condition at resonance: (Formula presented.) by using Mawhin's coincidence degree theory. Here, (Formula presented.) is the standard Riemann–Liouville fractional derivative of order (Formula presented.), and (Formula presented.) is the Riemann–Stieltjes integral of (Formula presented.) with respect to (Formula presented.). Our choice of (Formula presented.) in the boundary condition can be any integer between 0 and (Formula presented.), which supplements many boundary conditions assumed in the literature. Several examples are given to strengthen our result.