Multi-point boundary value problems for a coupled system of nonlinear fractional differential equations

In this paper, we investigate the existence and uniqueness of solutions to the coupled system of nonlinear fractional differential equations {-D(0+)(v1)y(1)(t) = lambda(1)a(1)(t)f(y(1)(t), y(2)(t)), -D(0+)(v2)y(2)(t) = lambda(2)a(2)(t)g(y(1)(t),y(2)(t)), where D-0+(v) is the standard Riemann-Liouville fractional derivative of order v, t is an element of (0, 1), v(1), v(2) is an element of (n - 1, n] for n > 3 and n is an element of N, and lambda(1), lambda(2) > 0, with the multi-point boundary value conditions: y(1)(i) (0) = 0 = y(2)(i) (0), 0 <= i <= n - 2; D(0+)(beta)y(1)(1) = Sigma(m-2)(i=1) b(i)D(0+)(beta)y(1)(xi(i)); D(0+)(beta)y(2)(1) = Sigma(m-2)(i=1) b(i)D(0+)(beta)y(2)(xi(i)), where n -2 < beta < n - 1, 0 < xi(1) < xi(2) < ... <xi(m-2) < 1, b(i) >= 0 (i = 1,2,..., m-2) with rho(1) := Sigma(m-2)(i=1) b(i)xi(v1-beta-1)(i) < 1, and rho(2) := Sigma(m-2)(i=1) b(i)xi(v2-beta-1)(j) < 1. Our analysis relies on the Banach contraction principle and Krasnoselskii's fixed point theorem.