Existence and uniqueness of positive solutions for a singular fractional three-point boundary value problem

Abstract

We investigate the existence and uniqueness of positive solutions for the following singular fractional three-point boundary value problem Dα0+ u (t) +f (t,u (t)) = 0,0 < t < 1, u (0) = u’ (0) =u’’ (0) = 0,u’’ (1) = βu’’(η), where 3 <α ≤ 4, Dα0+ is the standard Riemann-Liouville derivative and f : (0,1] × [0,∞) → [0,∞) with limt→0+ f (t,·) = ∞ (i.e., f is singular at t=0). Our analysis relies on a fixed point theorem in partially ordered metric spaces.