Multiple solutions of nonlinear boundary value problems for fractional differential equations

In this paper, we study nonlinear boundary value problems of fractional differential equations. (0.1) ( D q 0+ x(t) = f(t, x(t)) t ? J = [0,T] g x(0), x(T), x(?)
= 0 ? ? [0,T], where D0+ denotes the Caputo fractional derivative, 0 < q ? 1. Some new results on the multiple solutions are obtained by the use of the Amann theorem and the method of upper and lower solutions. An example is also given to illustrate our results. 2010 Mathematics Subject Classification: 26A33, 34K37