Abstract: By the means of the Green's function, the boundary value problem of fractional differential equation can be reduced to the equivalent integral equation. Recently, this method is used successfully to discuss the existence of the solution to boundary value problem of nonlinear fractional differential equation. By applying Carathéodory conditions and continuous condition on the nonlinear terms f , we obtain an existence results for solution. Our analysis relies on the concept of measures of noncompactness, the Mönch ′ s fixed point theorem and the Schaefer's fixed point theorem. Example is provided to illustrate the theory
