Existence of positive solutions for nonlinear fractional functional differential equation
In this paper, the existence of positive solutions for the nonlinear Caputo fractional functional differential equation in the form {D(0+)(q)y(t) + r(t)f(y(t)) = 0, for all t is an element of (0, 1), q is an element of {n - 1, n], y((i))(0) = 0, 0 <= i <= n - 3, alpha y((n-2))(t) - beta y((n-1))(t) = eta(t), t is an element of [-tau, 0], gamma y((n-2))(t) - delta y((n-1))(t) = xi(t), t is an element of [1, 1 + a], is studied. By constructing a special cone and using Krasnosel'skii's fixed point theorem, various results on the existence of at least one or two positive solutions to the fractional functional differential equation are established. The main results improve and generalize the existing results. (C) 2012 Elsevier Ltd. All rights reserved.
positive solutions fractional functional differential equation fixed point caputo derivative boundary value problem