<p>The main objective of the present work was to study the existence and uniqueness of solutions for coupled systems of Riemann-Liouville fractional differential equations and to verify their continuous dependence on initial conditions for coupled systems. The results showed that Perov’s fixed point theorem in vector Banach spaces provides an existence and uniqueness solution for coupled systems. Furthermore, the results demonstrated that the proved nonlinear alternative of Leray-Schauder, generalized in Banach spaces, guarantees the existence of a solution for coupled systems. Finally, two examples illustrate that the theorem yields more accurate solutions for coupled systems of Riemann-Liouville fractional differential equations.</p>