Abstract
This paper is concerned with boundary value problems for system of nonlinear fractional differential equations involving the Caputo fractional derivatives
{(c)D(q1)u(t) + f(1)(t, u(t), v(t)) = 0, t is an element of [0, 1], (c)D(q2)u(t) + f(2)(t, u(t), v(t)) = 0, t is an element of [0, 1], u(0) - alpha u'(0) = u'(eta) = beta u(t) + gamma u ''(1) = 0, v(0) - alpha v'(0) = v'(eta) = beta v(t) + gamma v ''(1) = 0,
where D-c(q1) and D-c(q2) are the standard Caputo fractional derivatives of orders q(1) and q(2) respectively, with 2 < q(1), q(2) <= 3. The functions f(i) : [0, 1] x [0, infinity) x [0, infinity) -> [0, infinity) are continuous for i = 1, 2, alpha > 0, beta > 0, gamma > 0, eta is an element of (0, 1). Under the suitable conditions, the existence and multiplicity of positive solutions are established by using abstract fixed point theorems.