This paper investigates the existence and topological structure of solution sets for non-local fractional differential equations defined on the half-line in a Banach space, within the framework of the Riemann–Liouville fractional derivative. The main results are established using the Meir–Keeler fixed point theorem for condensing operators, combined with the measure of non-compactness technique. Furthermore, an illustrative example is provided to demonstrate the applicability and feasibility of the theoretical findings.