J. Nonl. Evol. Equ. Appl. 2013 (8), pp. 101-110, published on October 9, 2014:

An improved result on triple non-negative solutions for a class of higher-order fractional differential equations

Xiangshan Kong

Basic Science Department, Qingdao Binhai University, Qingdao 266555, P.R. China

Haitao Li

School of Control Science and Engineering, Shandong University, Jinan 250061, P.R. China

Received on December 18, 2012
Accepted on February 24, 2013

Communicated by Gaston M. N'Guérékata

Abstract.  This paper investigates the existence of triple non-negative solutions for a kind of higher-order nonlinear fractional differential equations by using Leggett-Williams fixed point theorem, and presents a new existence criterion. The fractional derivative here is the standard Riemann-Liouville one. A new approximation of the Green’s function is derived to facilitate the proof of the main results. The study of an illustrative example shows that the new existence criterion obtained in this paper improves the existing results to some extent.
Keywords: Triple non-negative solutions, Riemann-Liouville fractional derivative, Higher-order fractional differential equations, Leggett-Williams fixed point theorem.
2010 Mathematics Subject Classification:   34A08; 34B18.

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