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 , where , $D_{0^{+}}^{\alpha }$ is the standard Riemann-Liouville derivative and $f:(\mathrm{0,1}]\times [0,\infty )\to [0,\infty )$ with ${\lim \hspace{0.17em}}_{t\to 0^{+}}f(t,·)=\infty$ (i.e., $f$ is singular at $t=0$). Our analysis relies on a fixed point theorem in partially ordered metric spaces.