The existence results for a coupled system of nonlinear fractional differential equations with multi-point boundary conditions

Document Type: Research Paper

Authors

School of Mathematical Sciences and Computing Technology, Central South University, Changsha, Hunan 410083, P.R.China

Abstract

In this paper, we study a coupled system of nonlinear
fractional differential equations with multi-point boundary condi-
tions. The differential operator is taken in the Riemann-Liouville
sense. Applying the Schauder fixed-point theorem and the contrac-
tion mapping principle, two existence results are obtained for the
following system
D^{alpha}_{0+}x(t)=fleft(t,y(t),D^{p}_{0+}y(t)right), t in (0,1),
D^{beta}_{0+}y(t)=gleft(t,x(t),D^{q}_{0+}x(t)right), t in (0,1),
x(0)=x'(0)=x''(0)=cdots=x^{(m-2)}(0)=0, x(1)=lambda x(xi) ,0y(0)=y',(0)=y''(0)=cdots=y^{(m-2)},(0)=0, y(1)=lambda y(xi) , 0where m in mathbb{N}, m geq 2,alpha,,beta in (m-1,m) and alpha,beta,p,q,lambda satisfy certain conditions.

Keywords

Main Subjects



Volume 38, Issue 3
September and October 2012
Pages 607-624
  • Receive Date: 25 October 2010
  • Revise Date: 20 March 2011
  • Accept Date: 20 March 2011