Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation

Abstract

We are concerned with the existence and nonexistence of positive solutions for the nonlinear fractional boundary value problem: $D_{0+}^{\alpha} u(t) + \lambda a(t) f(u(t)) =0$ $0\lt t \lt 1$ $u(0) = u^\prime (0) = u^\prime (1) = 0$ where $2\lt \alpah \lt 3$ is a real number and $D_{0+}^{\alpha }$ is the standard Riemann-Liouville fractional derivative. Our analysis relies on Krasnoselskiis fixed point theorem of cone preserving operators. An example is also given to illustrate the main results.