Abstract
In this article, we consider the properties of Green's function for the nonlinear fractional differential equation boundary value problem where 1 < α < 2, 0 < β, η < 1, is the standard Riemann–Liouville derivative. Here our nonlinearity f may be singular at u = 0. As an application of Green's function, we establish some multiple positive solutions for singular positone and semipositone boundary value problems by means of the Leray–Schauder nonlinear alternative, a fixed-point theorem on cones, and also we give uniqueness of a solution for a singular problem by a mixed monotone method.
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