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 Existence of positive solutions to a boundary value problem for a delayed singular high order fractional differential equation with sign-changing nonlinearity Dongyue Liu,Kemei Zhang Keywords:Positive solution; fractional differential equation; delay; cone expansion and cone compression fixed point theorem; changing sign nonlinearity Abstract: In this paper, we discuss the existence of positive solutions to the boundary value problem for a high order fractional differential equation with delay and singularities including changing sign nonlinearity. By using the properties of the Green function, Guo-krasnosel'skii fixed point theorem, Leray-Schauder's nonlinear alternative theorem, some existence results of positive solutions are obtained, respectively.