In this article, we investigate new results of existence and uniqueness for systems of nonlinear coupled differential equations and inclusions involving Caputo-type sequential derivatives of fractional order and along with new kinds of coupled discrete (multi-points) and fractional integral (Riemann-Liouville) boundary conditions. Our investigation is mainly based on the theorems of Schaefer, Banach, Covitz-Nadler, and nonlinear alternatives for Kakutani. The validity of the obtained results is demonstrated by numerical examples.