Existence Results for Singular Boundary Value Problem of Nonlinear FractionalDifferential Equation

Abstract

By applying a fixed point theorem for mappings that are decreasing with respect to a cone, this paper investigates the existence of positive solutions for the nonlinear fractional boundary value problem: $D_{0^{+}}^{\alpha }u\left(t\right)+f(t,u(t\left)\right)=0$, $0<t<1$, $u\left(0\right)=u\text{'}\left(0\right)=u\text{'}\left(1\right)=0$, where $2<\alpha <3$, $D_{0^{+}}^{\alpha }$ is the Riemann-Liouville fractional derivative.