Existence and Uniqueness Results to a Coupled System of Fractional Order Boundary Value Problems by Topological Degree Theory

In this article, we study existence and uniqueness results for a coupled system of nonlinear fractional order differential subject to nonlinear more general four-point boundary condition of the following type {D-C(alpha) u(t) = f(t,u(t),v(t)), (C)D(beta)v(t) = g(t,u(t),v(t)), t is an element of I = [0,1], lambda(1)u(0) - gamma(1)u(eta) - mu(1)u(1) = phi(u), lambda(2)u(0) - gamma(2)u(eta) - mu(2)u(1) = psi(v), where 0<, 1 and f, gC([0, 1]x(2), ) are continuous and the nonlocal functions phi, : (I, ) are also continuous. The parameters , satisfy 0<<1, 0<<1, and (i), (i), (i)(i=1, 2) are real numbers. Some new existence and uniqueness results are developed for the coupled system using topological degree theory and some standard fixed point theorems. An example is also provided to illustrate our main result.