Positive solutions of the three-point boundary value problem for fractional-order differential equations with an advanced argument | Wang et al. Advances in Difference Equations 2011 2011 2 http content 2011 1 2 o Advances in Difference Equations a SpringerOpen Journal RESEARCH Open Access Positive solutions of the three-point boundary value problem for fractional-order differential equations with an advanced argument Guotao Wang 1 SK Ntouyas2 and Lihong Zhang1 Correspondence wgt2512@163. com 1School of Mathematics and Computer Science Shanxi Normal University Linfen Shanxi 041004 P. R. China Full list of author information is available at the end of the article SpringerOpen0 Abstract In this article we consider the existence of at least one positive solution to the three-point boundary value problem for nonlinear fractional-order differential equation with an advanced argument i CDau t a t f u 0 t 0 0 t 1 u 0 u 0 0 p u n u 1 where 2 a 3 0 h 1 0 p - cDa is the Caputo fractional derivative. Using the well-known Guo-Krasnoselskii fixed point theorem sufficient conditions for the existence of at least one positive solution are established. MSC 2010 34A08 34B18 34K37. Keywords Positive solution Three-point boundary value problem Fractional differential equations Guo-Krasnoselskii fixed point theorem Cone 1 Introduction The study of three-point BVPs for nonlinear integer-order ordinary differential equations was initiated by Gupta 1 . Many authors since then considered the existence and multiplicity of solutions or positive solutions of three-point BVPs for nonlinear integer-order ordinary differential equations. To identify a few we refer the reader to 2-13 and the references therein. Fractional differential equations arise in many engineering and scientific disciplines as the mathematical modeling of systems and processes in the fields of physics chemistry aerodynamics electrodynamics of complex medium polymer rheology etc. 14-17 . In fact fractional-order models have proved to be more accurate than integerorder models . there are more degrees of freedom in
