Existence of positive solutions for the boundary value problem of a nonlinear fractional differential equation

Abstract

In this paper, we deal with the following nonlinear fractional boundary value problem

                             D^a_o+u(t) +f(t, u(t))= 0,0 < t < 1,4 < α <-5,

                            u(0) = u (1) = u'(0)= u'(1)= u"(1)= 0
where D^a_o+is the standard Riemann-Liouville differential operator of order α . We give some properties of Green's function for the problem. By means of some fixed-point theorems on cone, some existence and multiplicity results of positive solutions are obtained. Moreover, some concrete examples are given respectively.