Uniqueness of positive solutions for boundary value problems of singular fractional differential equations

In this article, we study the existence and uniqueness of a positive solution for the singular nonlinear fractional differential equation boundary value problem where 3 < α ≤ 4 is a real number, is the Riemann–Liouville fractional derivative and f : (0, 1] × [0, +∞) → [0, +∞) is continuous, (i.e. f is singular at t = 0). Our analysis relies on a fixed point theorem in partially ordered sets. As an application, an example is presented to illustrate the main results.