The Existence of Solutions to a Class of Multi-point Boundary Value Problem of Fractional Differential Equation

In this paper,we consider the following multi-point boundary value problem of fractional differential equation Dα0+u(t) = f(t,u(t),Dα 10+u(t),Dα 20+u(t),Dα 30+u(t)),t ∈(0,1),mI4 α0+u(0) = 0,Dα 10+u(0) =i=1αiDα 10+u(ξi),Dα 20+u(1) =nj=1βjDα 20+u(ηj),Dα 30+u(1) Dα 30+u(0) = Dα 20+u(12),where 3 < α≤ 4 is a real number.By applying Mawhin coincidence degree theory and constructing suitable operators,some existence results of solutions can be established.