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.
Chen, Y., Chen, D., & Lv, Z. (2012). The existence results for a coupled system of nonlinear fractional differential equations with multi-point boundary conditions. Bulletin of the Iranian Mathematical Society, 38(3), 607-624.
MLA
Yi Chen; Dezhu Chen; Zhanmei Lv. "The existence results for a coupled system of nonlinear fractional differential equations with multi-point boundary conditions". Bulletin of the Iranian Mathematical Society, 38, 3, 2012, 607-624.
HARVARD
Chen, Y., Chen, D., Lv, Z. (2012). 'The existence results for a coupled system of nonlinear fractional differential equations with multi-point boundary conditions', Bulletin of the Iranian Mathematical Society, 38(3), pp. 607-624.
VANCOUVER
Chen, Y., Chen, D., Lv, Z. The existence results for a coupled system of nonlinear fractional differential equations with multi-point boundary conditions. Bulletin of the Iranian Mathematical Society, 2012; 38(3): 607-624.