Abstract

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: by using Mawhin's coincidence degree theory. Here, is the standard Riemann–Liouville fractional derivative of order , and is the Riemann–Stieltjes integral of with respect to . Our choice of in the boundary condition can be any integer between 0 and , which supplements many boundary conditions assumed in the literature. Several examples are given to strengthen our result.

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