Abstract
In this paper, we attempt to establish the existence of at least three positive solutions for a coupled system of p-Laplacian fractional order boundary value problems
{D-a+(beta 1) (phi(p)(D-a+(alpha 1) u(t))) = f(1)(t, u(t), v(t)) a < t < b, D-a+(beta 2) (phi(p)(D-a+(alpha 2) u(t))) = f(2)(t, u(t), v(t)) a < t < b,
with the boundary conditions
{u((j))(a) = 0, j = 0, 1, 2, ..., u '' (b) = delta u ''(xi), phi(p)(D(a+)(alpha 1)u(a)) = 0, phi(p)(D(a+)(alpha 1)u(a)) = 0, phi(p)(D(a+)(alpha 1)u(b)) = theta phi(p)(D(a+)(alpha 1)u(eta)), v((j)) (a) = 0, j = 0, 1, 2, ..., v '' (b) = delta v ''(xi), phi(p)(D(a+)(alpha 2)v(a)) = 0, phi(p)(D(a+)(alpha 2)v(b)) = theta phi(p)(D(a+)(alpha 2)v(eta)),
by applying the five functional fixed point theorem.