Existence of Positive Solutions for Fractional Differential Equation with Nonlocal Boundary Condition

By using the fixed point theorem, existence of positive solutions for fractional differential equation with nonlocal boundary condition D-0+(infinity) u(t) + a(t) f(t, u(t)) = 0, 0 < t < 1, u(0) = u(1) = Sigma(infinity)(i-1)alpha(i)u(xi(i)) is considered, where 1 < alpha <= 2 is a real number, Da(0+)(alpha) is the standard Riemann-Liouville differentiation, and xi(i) epsilon (0, 1) , alpha(i) epsilon [0, infinity) with Sigma(infinity)(i=1) alpha(i)xi(alpha-1)(i) < 1, a(t) epsilon C([0, 1], [0, infinity], f(t, u)) epsilon C([0, 1] x [0, infinity),[0, infinity)).