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

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.