Open Access Research

Nontrivial solutions for a higher fractional differential equation with fractional multi-point boundary conditions

Min Jia1*, Xinguang Zhang2* and Xuemai Gu1

Author Affiliations

1 Communication Research Center, Harbin Institute of Technology, Harbin, 150080, China

2 School of Mathematical and Informational Sciences, Yantai University, Yantai, 264005, China

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Boundary Value Problems 2012, 2012:70  doi:10.1186/1687-2770-2012-70

Published: 3 July 2012

Abstract

This paper investigates the existence and uniqueness of nontrivial solutions to a class of fractional nonlocal multi-point boundary value problems of higher order fractional differential equation, this kind of problems arise from viscoelasticity, electrochemistry control, porous media, electromagnetic and signal processing of wireless communication system. Some sufficient conditions for the existence and uniqueness of nontrivial solutions are established under certain suitable growth conditions, our proof is based on Leray-Schauder nonlinear alternative and Schauder fixed point theorem.

MSC: 34B15, 34B25.

Keywords:
fractional differential equation; nontrivial solution; Green function; Leray-Schauder nonlinear alternative