Positive Solutions for Coupled Nonlinear Fractional Differential Equations

Abstract

We consider the existence of positive solutions for a coupled system of nonlinear fractional differential equations with integral boundary values. Assume the nonlinear term is superlinear in one equation and sublinear in the other equation. By constructing two cones $K_1$, $K_2$ and computing the fixed point index in product cone $K_1\times K_2$, we obtain that the system has a pair of positive solutions. It is remarkable that it is established on the Cartesian product of two cones, in which the feature of two equations can be opposite.