一类非线性分数阶微分方程边值问题解的存在性  

Existence of Solution to Boundary Value Problem for Nonlinear Fractional Differential Equation

作　　者：张海丽[1] ZHANG Haili(Foundation Department, Shanxi Traffic Vocational and Technical College, Taiyuan, Shanxi 030031, China)

机构地区：[1]山西交通职业技术学院基础部,山西太原030031

出　　处：《宜宾学院学报》2017年第12期78-81,91,共5页Journal of Yibin University

基　　金：山西省自然基金项目(2010011028)

摘　　要：利用锥拉伸和压缩不动点定理研究了非线性分数阶微分方程边值问题:﹛~cD_(0^+)~αu(t)=λf(t,u(t),u'(t)),0<t<1u(0)=u'(0)=u(1)=0得到解的存在性,其中0<λ<1,2<α≤3,f∈C([0,1]×R^2,R),~cDD_(0^+)~α为Caputo型分数阶微分.By using fixed point theory of cone expansion and compression of norm type,the existence of solutions for nonlinear fractional differential equation:cDα0+u(t)=λf(t,u(t),u'(t)),0<t<1u(0)=u'(0)=u(1)=0was investigated,where0<λ<1,2<α≤3,f∈C([0,1]×R2,R),cDDα0+is the Caputo fractional derivative.

关 键 词：分数阶微分方程 边值问题 不动点定理 

分 类 号：O175.8[理学—数学]