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分数阶微分方程边值问题正解的唯一性(英文) 被引量：3

Unique Positive Solution of Boundary Value Problem for Fractional Differential Equations
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摘要 分数阶微分方程在生物科学和其他领域发挥着重要作用.考虑来类分数阶微分方程边值问题正解的这来性,得到的结证不仅可以保证正解的存在这来,而且可以用于构造迭代序列来逼近这个解. Fractional differential equations play an important role in biological sciences and other fields.In this paper,we consider the uniqueness of positive solution for boundary value problem of fractional differential equation.Our results can not only guarantee the existence of unique positive solution,but also be applied to construct an iterative schemes to approximate it.
作者 杨柳 陈海波
机构地区 衡阳师范学院数学与计算科学系 中南大学数学科学与计算技术学院
出处 《生物数学学报》 CSCD 北大核心 2011年第1期43-47,共5页 Journal of Biomathematics
基金 The National Natural Science Foundation of China(no.10871206) Cultivation to Young Teacher Foundation of Hengyang Normal University(2008)
关键词 Riemann-Liouville导数 分数阶微分方程 正解 Riemann-Liouville differentiation Fractional differential equation Positive solution
分类号 O175.12 [理学—基础数学]
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  • 1苏新卫,穆晓霞.非线性分数阶微分方程系统正解的存在性和唯一性[J].河南师范大学学报（自然科学版）,2006,34(4):9-12. 被引量：8
  • 2Kilbas A A, Srivastava H M, Trujillo J ,J. Theory and Applications of Fractional Differential Equa.tions[M],Elsevier B. V., Amsterdam, 2006.
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  • 4Samko S G, Kilbas A A, Marichev O I. Fractional Integral And Derivatives(Theory and Applications)[M].Switzerland: Gordon and Breach, 1993.
  • 5Bai C Z, Fang J X. The existence of a positive solution for a singular couplcd system of a nonlinear fractionaldifferential equation[J]. Applied Mathematics and Computation, 2004, 35(3):611-621.
  • 6Su X. Boundary value problem for a coupled system of nonlinear fractional differential equditions[J].AppliedMathematics Letters, 2009,35(22): 64-69.
  • 7Bai Z B, LV H S. Positive solutions for boundary value problem of nonlinear fractional differential equation [J].Jom'nal of Mathematical Analysis and Application, 2005, 35(311):495-505.
  • 8Liang S, Zhang J. Positive solutions for boundary problems of nonlinear fractional differential equation[J].Nonlinear Analysis, 2009, 35(71):5545-5550.
  • 9Amini-Harandi A, Emani H. A fixed point theorem for contraction type maps in partially ordered metricspaces and application to ordinary differential cquations[J]. Nonlinear Analysis, 2010, 35(72):2238--2242.
  • 10BAI Z B. Positive solutions for boundary value problem of nonlinear fractional equation[J]. Journal of Mathematical Analysis and Applications, 2005, 311:495-505.

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生物数学学报
2011年 第1期

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