The existence of positive solutions for high order fractional differential equations with sign changing nonlinearity and parameters

By constructing an auxiliary boundary value problem, the difficulty caused by sign changing nonlinearity terms is overcome by means of the linear superposition principle. Using the Guo-Krasnosel'skii fixed point theorem, the results of the existence of positive solutions for boundary value problems of high order fractional differential equation are obtained in different parameter intervals under a more relaxed condition compared with the existing literature. As an application, we give two examples to illustrate our results.