On a coupled system of nonlinear generalized fractional differential equations with nonlocal coupled Riemann-Stieltjes boundary conditions (Q6562448)

In this paper, by applying the fixed point approach the authors study the existence and uniqueness of solutions for a generalized coupled fractional differential system with nonlinearities depending upon the unknown functions together with their lower order generalized fractional derivatives, and subject to nonlocal coupled Riemann-Stieltjes and generalized fractional integral boundary conditions. The uniqueness of solutions is established with the aid of a fixed point theorem due to Banach, while the second result ensuring the existence of solutions for the given problem was obtained by using the Leray-Schauder alternative. An example illustrating the obtained results is also presented.