Positive Solutions to m-point Boundary Value Problem of Fractional Differential Equation

In this paper, we study the multiplicity of positive solutions to the following m-point boundary value problem of nonlinear fractional differential equations: {Dqu(t) + f(t, u(t)) = 0, 0 < t < 1, u(0) = 0, u(1) = Sigma(m-2)(i-1) mu(i)D(p)u(t)vertical bar(t=xi i). where q is an element of R, 1<q <= 2, 0 xi 1<xi 2<...<xi(m-2)<= 1/2, mu(i)is an element of(0, + infinity) and p = q-1/2, Gamma(q) Sigma(m-2)(i=1) < Gamma(q+1/2), D-q is the standard Riemann-Liouville differentiation, and f is an element of C[0,1]x[0,+infinity)). By using the Leggett-Williams fixed point theorem on a convex cone, some multiplicity results of positive solutions are obtained.