Multiple Positive Solutions to Nonlinear Boundary Value Problems of a System for Fractional Differential Equations

By using Krasnoselskii's fixed point theorem, we study the existence of at least one or two positive solutions to a systemof fractional boundary value problems given by -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, v(1), v(2) epsilon (n - 1, n] for n > 3 and n epsilon N, subject to the boundary conditions y(1)((i))(0) = 0 = y(2)((i))(0), for 0 <= i <= n - 2, and [D-0+(alpha) y(2)(t)](t=1) = 0 = [D(0+)(alpha)y(2)(t)](t=1), for 1 <= alpha <= n - 2, or y(1)((i))(0) = 0 = y(2)((i))(0), for 0 <= i <= n - 2, and [D(0+)(alpha)y(1)(t)](t=1) = phi(perpendicular to) (y(perpendicular to)), [D(0+)(alpha)y(2)(t)](t=1) = phi(2) (y(2)), for 1 <= alpha <= n - 2, phi(1), phi(2) epsilon C([0,1], R). Our results are new and complement previously known results. As an application, we also give an example to demonstrate our result.