Existence, uniqueness, and positive solutions to a nonlinear fractional boundary value problem

Abstract

Using Banach’s contraction principle and Schauder’s fixed point theorem, the authors establish results on the existence and uniqueness of solutions to a fractional boundary value problem of order 1 <γ≤ 2. They also use the Avery–Peterson fixed point theorem to prove the existence of multiple positive solution to the problem. As an application, they prove the existence of at least two positive solutions to a model of hematopoiesis (red blood cell production).