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偏序度量空间上压缩映像不动点定理在分数阶微分方程边值问题上的应用

Applications of a Fixed Point Theorem for Generalized Contraction in Partially Ordered Complete Metric Spaces to Boundary Value Problem of Fractional Differential Equations
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摘要 用偏序度量空间上的压缩映像不动点定理研究分数阶两点边值问题:D0-αu(t)=f(t,u(t)),0t1, u(0) =u(1) =u'(0) =u'(l) =0其中:3〈α≤4是实数;D0^a+是标准的Riemann—Liouville微分.证明了上述两点边值问题正解的存在唯一性. We gave an existence and uniqueness for the solution of a nonlinear fractional differential equation boundary value problem D0-αu(t)=f(t,u(t)),0t1, u(0) =u(1) =u'(0) =u'(l) =0, where 3α≤4 is a real number,and D(0+)αis the standard Riemann-Liouville differentiation.Our result relies on a fixed point theorem for generalized contraction in partially ordered complete metric spaces.
出处 《吉林大学学报(理学版)》 CAS CSCD 北大核心 2013年第3期423-426,共4页 Journal of Jilin University:Science Edition
基金 国家自然科学基金(批准号:10571021:10701020) 中央高校基本科研业务费专项基金(批准号:13CX02015A) 吉林省教育厅"十二五"科学技术研究项目(批准号:吉教科合字[2013]第505号)
关键词 分数阶微分方程 边值问题 正解 偏序度量空间 不动点定理 fractional differential equation boundary value problem positive solution partially ordered metric spaces fixed-point theorem
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