Existence Solution for Two-point Boundary Value Problem of a Fractional Differential Equation with 2 < α≤3

By applying the schauder fixed-point theorem and the nature of Green function, the authors attained an existence solution for two-point boundary value problem of a fractional differential equation \left\\beginarraylD_0+ ^\alpha u(t)=f\left(t, u(t), ^c D_0+ ^\beta u(t)\right), 0 \leqslant t \leqslant 1 \ u(0)=u(1)=u(0)=0, 2<\alpha \leqslant 3, 0<\beta \leqslant 1\endarray\right., where D0+α is the Riemann-Liouvill Fractional differentiation and cD0+β is the caputo's Fractional differentiation.