Abstract
In this paper, we study the following fractional order three-point boundary value problem
{D-0+(q1) u(t) + f(t, u(t)) = 0, t is an element of[0,1] u(0) - alpha D-0+(q2) u(0) = D-0+(q2) u(eta) = beta u(1) + gamma D-0+(q3) u(1) = 0
where D-0+(qi), i = 1, 2, 3, are the standard Riemann-Liouville fractional order derivatives with 2 < q(1) <= 3, 0 < q(2) = 1, 1 < q(3) <= 2 and a > 0, alpha > 0, beta > 0, eta is an element of(0, 1) and f: [0, 1] x [0, infinity] -> [0, infinity] is continuous. By using several well-known fixed-point theorems in a cone, the existence of at least one and two positive solutions is obtained. Some examples are presented to illustrate the main results.