Positive solutions for a class of singular fractional boundary value problems

Abstract

In this paper, we investigate the existence and uniqueness of positive solutions for the following singular fractional boundary value problem D0 +αu(t)+f(t,u(t))=0,0<t<1,u(0)=u(1)=0, where 1<α≤2, D0+α is the standard Riemann-Liouville differentiation and f(0,1]×[0,∞)[0,∞) with lim t→0 + f(t,-)=∞ (i.e., f is singular at t=0). Our analysis relies on a fixed point theorem in partially ordered sets.