Positive solutions for boundary value problems of singular fractional differential system

摘要：

Existence of positive solution to a fractional singular system with four-point coupled boundary conditions of the type-Dαtx(t)=f(t,x(t),y(t)),t∈(0,1),-Dαty(t)=g(t,x(t),y(t)),t∈(0,1),x(0)=0,x(1)=λ1y(ζ),y(0)=0,y(1)=λ2x(η),is established, where the fractional derivative is in the sense of Caputo and 1<α<2.The nonlinearities f,g:(0,1)×0,∞)×0,∞)→0,∞)are continuous and singular at t = 0; t = 1,while the parameters λ1,λ2,ζ,η satisfy ζ,η∈(0,1),0<λ1,λ2ζη<1.The peculiarity of this system is that the nonlinear terms are singular, compared with the available results in literature. The proof of our main result is based on the Guo-Krasnoselskii ˉxed-point theorem. An example is included to show the applicability of our result.

关键词： Caputo fractional derivative Positive solutions Coupled singular system Coupled four-point boundary conditions Fixed point theorem.

作者: Zhoujin Cui Pinneng Yu Rui Zhang

作者单位: Institute of Science, PLA University of Science and Technology,Nanjing 211101, China Department of Basic Education, Jinling Institute of Technology, Nanjing 211100 , China

会议类型: 国际会议

会议名称: The Fifth Symposium on Fractional Differentiation and Its Applications(第五届国际自动控制联合会分数阶导数及其应用会议)

会议地点: 南京

会议语种:英文

页码: 1-6

在线出版日期: 2012-05-14（万方平台首次上网日期，不代表论文的发表时间）