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

Abstract

We are concerned with the existence and uniqueness of positive solutions for the following nonlinear fractional boundary value problem: D 0+ α u (t) + f (t, u (t)) = 0, 0 ≤ t ≤ 1, 3 < α ≤ 4, u (0) = u ′ (0) = u″ (0) = u″ (1) = 0, where D0+ α 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.