This paper presents a K-dimensional system of an anti-periodic boundary value problem for nonlinear fractional differential equations with Riemann–Liouville–Caputo derivatives. Here, we will study inequalities such as the new fractional Grunwald and several fixed point theorems, as well as some results on the existence of solutions that Lipschitz holds. In the examples section, we had three examples that will group the results obtained for a specific two-dimensional case in a table and draw their graphs to better display the relationships and results. We also discussed the existence and uniqueness of a system of fractional differential equations to model a financial problem. In fact, by applying Caputo's fractional derivative, we have obtained a new financial model.
