Existence and uniqueness of positive solution for a boundary value problem of fractional order (Q554856)

Summary: We are concerned with the existence and uniqueness of positive solutions for the following nonlinear fractional boundary value problem: \(D^{\alpha}_{0+}u(t) + f(t, u(t)) = 0, 0 \leq t \leq 1, 3 < \alpha \leq 4\), \(u(0) = u'(0) = u''(0) = u''(1) = 0\), where \(D^{\alpha}_{0+}\) denotes the standard Riemann-Liouville fractional derivative. Our analysis relies on a fixed point theorem in partially ordered sets. Some examples are also given to illustrate the results.