The Positive Properties of Green’s Function for Fractional Differential Equations and Its Applications

Abstract

We consider the properties of Green’s function for the nonlinear fractional differential equation boundary value problem: , where , ${\mathbf{D}}_{0+}^{\alpha }$ is the standard Riemann-Liouville derivative. Here our nonlinearity $f$ may be singular at $u=0$. As applications of Green’s function, we give some multiple positive solutions for singular boundary value problems by means of Schauder fixed-point theorem.