# Existence and uniqueness of positive and nondecreasing solution for nonlocal fractional boundary value problem

Document Type : Research Paper

Authors

1 Department of Mathematics, Neka Branch, Islamic Azad University, Neka, Iran

2 Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran

Abstract

In this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form $D_{0^{+}}^{alpha}x(t)+f(t,x(t))=0, 0<t<1, 2<alpha<3, x(0)= x'(0)=0, x'(1)=beta x(xi)$, where $D_{0^{+}}^{alpha}$ denotes the standard Riemann-Liouville fractional derivative,$0<xi<1$ and $0<\beta\xi^{\alpha-1}<\alpha-1$ Our analysis relies a fixed point theorem in partially ordered sets. An illustrative example is also presented.

Keywords

### History

• Receive Date: 14 September 2015
• Revise Date: 26 March 2016
• Accept Date: 02 April 2016