Positive solutions for boundary value problem of nonlinear fractional differential equation. (English) Zbl 1149.26012

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.


26A33 Fractional derivatives and integrals
34K10 Boundary value problems for functional-differential equations
Full Text: EuDML