Existence and uniqueness of monotone positive solutions for fractional higher-order BVPs

Abstract

We discuss the existence and uniqueness of monotone positive solutions for a class of higher-order nonlinear fractional differential equations infinite-point boundary value problems (for short, BVPs) on cones. The existence and uniqueness of solutions are obtained via applying the properties of the Green function and a fixed point theorem. Our analysis is based on the operator equation $T\omega +S\omega =\omega$ on an ordered Banach space. Finally, a example is given to illustrate our results.