In this paper, we study existence and multiplicity results for a coupled system of nonlinear nonlocal boundary value problems for higher order fractional differential equations of the type (see PDF) where (see PDF) is Caputo fractional derivative. We employ the Guo-Krasnosel’skii fixed point theorem to establish existence and multiplicity results for positive solutions. We derive explicit intervals for the parameters _ and μ for which the system possess the positive solutions or multiple positive solutions. Examples are included to show the applicability of the main results.