Positive solutions for boundary value problem of nonlinear fractional differential equation (Q5920444)

Summary: We are concerned with the existence and nonexistence of positive solutions for the nonlinear fractional boundary value problem: \(D_{0+}^{\alpha}u(t)+\lambda a(t) f(u(t))=0\), \(0<t<1\), \(u(0)=u'(0)=u'(1)=0\), where \(2<\alpha<3\) 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.