A coincidence point theorem and its applications to fractional differential equations

Abstract

We establish a coincidence point theorem in complete metric spaces. As a consequence, we show the existence of solutions to a system of initial value problem of fractional differential equations involving Riemann–Liouville fractional derivatives. Next, we derive several coincidence point theorems for new classes of sublinear and superlinear operators, in the context of ordered Banach spaces. Finally, we apply these results to discuss the existence of positive solutions to a class of initial value problem of fractional differential equations.