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 The existence of nontrivial solution for boundary value problem of nonlinear fractional differential equation Yan Bai,Weihua Jiang,Yanping Guo,Yunhong Li,Yujing Liu Keywords:fractional differential equation, eigenvalue, Green's function, Leray-Schauder degree. Abstract: By using the theory of degree, the existence of nontrivial solution for boundary value problem of nonlinear fractional differential equation is investigated. In order to get this conclusion, we make use of Laplace transform to obtain the conditions that the eigenvalues satisfy. Then, for three different specific problems, we use Matlab software to calculate the eigenvalues. This is the fundamental skill that Leray-Schauder degree theorem can be used.