The existence of positive solutions for boundary value problem of nonlinear fractional differential equations (Q1724729)

Summary: We consider the existence of positive solutions for the nonlinear fractional differential equations boundary value problem \(-D_{0^+}^\alpha u(t)=f(t,u(t))\), \(0<t<1\), \(u(0)=u'(0)=u'(1)=0\), where \(2<\alpha\leq3\) is a real number, \(D_{0^+}^\alpha\) is the Riemann-Liouville fractional derivative of order \(\alpha\), and \(f\) is a given continuous function. Our analysis relies on the fixed point index theory in cones.