An existence result for a superlinear fractional differential equation

Abstract

We establish the existence and uniqueness of solution for the boundary value problem (0)D(t)(alpha)(x') + a(t)x(lambda) = 0, t > 0, x' (0) = 0, lim(t ->+infinity) x(t) = 1, where (0)D(t)(alpha) designates the Riemann-Liouville derivative of order alpha epsilon (0, 1) and lambda > 1. Our result might be useful for establishing a non-integer variant of the Atkinson classical theorem on the oscillation of Emden-Fowler equations