The Existence of Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equations.

We consider the existence of positive solutions for the nonlinear fractional differential equations boundary value problem -D0+α u(t) = f(t,u(t)), 0 < t < 1, u(0) = u'(0) = u'( 1) = 0, where 2 < α ≤ 3 is a real number, D0+α is the Riemann-Liouville fractional derivative of order α, and f is a given continuous function. Our analysis relies on the fixed point index theory in cones. [ABSTRACT FROM AUTHOR]