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In this paper, we consider the properties of Green's function for the singular nonlinear fractional differential equation boundary value problem equation presented, where 3 < α ≤ 4 is a real number and D α 0+ is the standard Riemann-Liouville differentiation. As an application of the properties of Green's function, we give the existence of multiple positive solutions for the above mentioned singular boundary value problems. Our tools are Leray-Schauder nonlinear alternative and Krasnoselskii's fixed-point theorem on cones. © 2013 Jin and Lin; licensee Springer.

Positive properties of Green’s function for focal-type BVPs of singular nonlinear fractional differential equations and its application