title: Some existence results on nonlinear fractional differential equations.
abstract: In this paper, by using fixed-point methods, we study the existence and uniqueness of a solution for the nonlinear fractional differential equation boundary-value problem D(α)u(t)=f(t,u(t)) with a Riemann-Liouville fractional derivative via the different boundary-value problems u(0)=u(T), and the three-point boundary condition u(0)=β(1)u(η) and u(T)=β(2)u(η), where T>0, t∈I=[0,T], 0<α<1, 0<η<T, 0<β(1)<β(2)<1.
authors.affiliation: Department of Mathematics, Cankaya University, 06530 Balgat, Ankara, Turkey. dumitru@cankaya.edu.tr
authors.forename: Dumitru
authors.initials: D
authors.lastname: Baleanu
authors.forename: Shahram
authors.initials: S
authors.lastname: Rezapour
authors.forename: Hakimeh
authors.initials: H
authors.lastname: Mohammadi