Author/Authors :
Chen, Yi Central South University - School of Mathematics and Statistics, China , Chen, Dezhu Central South University - School of Mathematics and Statistics, China , Lv, Zhanmei Central South University - School of Business, China
Abstract :
In this paper, we study a coupled system of nonlinear fractional differential equations with multi-point boundary conditions. The differential operator is taken in the Riemann-Liouville sense. Applying the Schauder fixed-point theorem and the contraction 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 element of (0,1), D^{beta}_{0+}y(t)=gleft(t,x(t),D^{q}_{0+}x(t)right), t element of (0,1), x(0)=x (0)=x (0)=cdots=x^{(m-2)}(0)=0, x(1)=lambda x(xi) , y(0)=y ,(0)=y (0)=cdots=y^{(m-2)},(0)=0, y(1)=lambda y(xi) , where 0˂ xi ˂ 1, m element of mathbb{N}, m geq 2,alpha,,beta in (m-1,m) and alpha,beta,p,q,lambda satisfy certain conditions.
Keywords :
Fractional differential equations , Boundary value problem , Schauder fixed , point theorem , Contraction mapping principle
