Positive solutions for a fractional boundary value problem via a mixed monotone operator

Abstract

In this paper, by using a mixed monotone operator method we study the existence and uniqueness of positive solutions to the following nonlinear fractional boundary value problem (Formula presented)where (Formula presented) denotes de Caputo fractional derivative, f: [0, 1] × [0, ∞) × [0, ∞) → [0, ∞) and g: [0, 1] × [0, ∞) → [0, ∞) are continuous functions and H is an operator (not necessarily linear) applying C[0, 1] into itself. Moreover, in order to illustrate our results, we present some examples.