Abstract
We investigate a coupled system of fractional differential equations with nonlinearities depending on the unknown functions as well as their lower order fractional derivatives supplemented with coupled nonlocal and integral boundary conditions. We emphasize that the problem considered in the present setting is new and provides further insight into the study of nonlocal nonlinear coupled boundary value problems. We present two results in this paper: the first one dealing with the uniqueness of solutions for the given problem is established by applying contraction mapping principle, while the second one concerning the existence of solutions is obtained via Leray–Schauder’s alternative. The main results are well illustrated with the aid of examples.