An Existence Result for a Superlinear Fractional Differential Equation

Abstract

We establish the existence and uniqueness of solution for the boundary value problem D-0(t)alpha(x') + a(t)x(lambda) = 0, t > 0, x' (0) = 0, lim(t ->+infinity) x(t) = 1, where D-0(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. (C) 2010 Elsevier Ltd. All rights reserved.