Existence and uniqueness of solutions for fractional differential system with four-point coupled boundary conditions

The goal of this paper is to study the existence and uniqueness of solutions for fractional differential system with four-point coupled boundary conditions of the type: D(0+)(alpha 1)u(1)(t) + f(1)(t, u(1)(t), u(2)(t)) = 0, u(1)(0) = u '(1)(0) = 0, u(1)(1) = a(1)u(2)(xi(1)), D(0+)(alpha 2)u(2)(t) + f(2)(t, u(1)(t), u(2)(t)) = 0, u(2)(0) = u '(2)(0) = 0, u(2)(1) = a(2)u(1)(xi(2)). Our hypotheses on the nonlinearities f(1) and f(2) are formulated with a mild Lipschitz assumption. The main tools used are spectral analysis of matrices and Perov's fixed point theorem. An example is also given to illustrate the applicability of the results.