| Abstract: | We study the boundary value problem of a coupled differential system of fractional order, and prove the existence and uniqueness of solutions to the considered problem. The underlying differential system is featured by a fractional differential operator, which is defined in the Riemann-Liouville sense, and a nonlinear term in which different solution components are coupled. The analysis is based on the reduction of the given system to an equivalent system of integral equations. By means of the nonlinear alternative of Leray-Schauder, the existence of solutions of the factional differential system is obtained. The uniqueness is established by using the Banach contraction principle. |
