Existence and Uniqueness of Positive Solution for a Boundary Value Problem of Fractional Order

Abstract

We are concerned with the existence and uniqueness of positive solutions for the following nonlinear fractional boundary value problem: D0+αu(t)+f(t,u(t))=0, 0≤t≤1, 3<α≤4, u(0)=u′(0)=u″(0)=u″(1)=0, where D0+α denotes the standard Riemann-Liouville fractional derivative. Our analysis relies on a fixed point theorem in partially ordered sets. Some examples are also given to illustrate the results.