Well-posedness of a kind of nonlinear coupled system of fractional differential equations  

作　　者：ZHOU XiaoJun XU ChuanJu 

机构地区：[1]School of Mathematical Sciences, Xiamen University [2]School of Mathematics and Computer Science, Guizhou Normal University

出　　处：《Science China Mathematics》2016年第6期1209-1220,共12页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11471274,11421110001 and 91130002);Natural Science Foundation of Guizhou Province(Grant No.LKS[2013]04)

摘　　要：We study the boundary value problem of a coupled differential system of fractional order, and prove the existence and uniqueness of solutions to the considered problem. The underlying differential system is featured by a fractional differential operator, which is defined in the Riemann-Liouville sense, and a nonlinear term in which different solution components are coupled. The analysis is based on the reduction of the given system to an equivalent system of integral equations. By means of the nonlinear alternative of Leray-Schauder,the existence of solutions of the factional differential system is obtained. The uniqueness is established by using the Banach contraction principle.We study the boundary value problem of a coupled differential system of fractional order, and prove the existence and uniqueness of solutions to the considered problem. The underlying differential system is featured by a fractional differential operator, which is defined in the Riemann-Liouville sense, and a nonlinear term in which different solution components are coupled. The analysis is based on the reduction of the given system to an equivalent system of integral equations. By means of the nonlinear alternative of Leray-Schauder,the existence of solutions of the factional differential system is obtained. The uniqueness is established by using the Banach contraction principle.

关 键 词：fractional differential equations nonlinear coupled system existence and uniqueness of solutions 

分 类 号：O175.29[理学—数学]