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分数阶微分方程边值问题解的存在性及唯一性 被引量：6

Existence and Uniqueness of Solutions for the Fractional Differential Equations
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摘要 研究了一类带有积分边值条件的分数阶微分方程两点边值问题.在一定条件下,利用压缩映像原理及Krasnoselskii不动点定理,得到了分数阶微分方程积分边值问题解的存在性及唯一性. This paper investigates a class of two-point boundary value problem for fractional differential equations with integral boundary value condition.By using the contraction mapping principle and Krasnoselskii fixed point theorem,existence and uniqueness of solutions for the fractional differential equations with integral boundary value problem are obtained.
作者 华守亮 吕志伟
机构地区 安阳工学院数理系
出处 《河南大学学报（自然科学版）》 CAS 北大核心 2010年第5期453-455,共3页 Journal of Henan University:Natural Science
基金 安阳工学院优秀青年骨干教师基金(200712)
关键词 分数阶微分方程 不动点定理 存在性 fractional differential equations fixed point theorem existence of solutions
分类号 O175.1 [理学—基础数学]
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参考文献5

  • 1Kilbas A A, Srivastava H M, Trujillo. J.J. Theory and Applications of Fractional Differential Equations[M]// North- Holland Mathematics Studies. Amsterdam: Elsevier, 2006.
  • 2Podlubny. I. Fractional Differential Equations[M]. New York: Academic press, 1993.
  • 3Zhanbing Bai, Haishen I.u, Positive solutions for boundary value problem of nonlinear fractional differential equation[J]. J. Math. Anal. Appl. , 2005(31):1495-505.
  • 4Daqing Jiang, Chengjun Yuan. The positive properties of the Green funtion for Dirichlet-type boundary value problems of nonlinear fractional differential equations and its application[J]. Nonlinear Anal. , 2010,72:710-719.
  • 5Xiaojie Xu, Daqing Jiang, Chengjun Yuan. Muhiple positive solutions for the boundary value problem of a nonlinear fractional differential equation[J]. Nonlinear Anal. , 2009,71:4626-4688.

同被引文献25

  • 1章美月,刘文斌.分数阶微分方程积分边值问题解的存在性[J].应用泛函分析学报,2013,15(2):167-171. 被引量：2
  • 2K ILBAS A A,SR IVASTAVA,TRU JILLO J J.Theory and applications of fractional different ial equations. . 2006
  • 3LAKSHMIKANTHAM V,VATSALA A S.Basic theory of fractionald ifferential equation. Nonlinear Analysis . 2008
  • 4ZHANG Shuqin.The existence of a positive solu tion for a non l inearfractional d ifferent ial equat ion. JMath AnalAppl . 2000
  • 5Z.Bai,T.Qiu.Existence of positive solution for singular fractional differential equation. Applied Mathematics Letters . 2009
  • 6Delbosco D,Rodino L.Existence and uniqueness for a nonlinear fractional differential equation. Journal of Mathematical . 1996
  • 7Kilbas A A, Srivastava H M, Trujillo J J. Theory and Applications of Fractional Differential Equa- tions[M]. North-Holl and Mathematics Studies, Amsterdam: Elsevier, 2006.
  • 8Podlubny I. Factional Differential Equations[M]. New York: Academic Press, 1993.
  • 9Jiang D (Qa, Yuan C J. The positive properties of the Green function for Dirichlet type bound- ary value problems of nonlinear fractional differential equations and its application[J]. Nonlinear Analysis, 2010(72): 710-719.
  • 10Bai Z B, Lu H S. Positive solutions for boundary value problem of nonlinear fractional differential equation[J]. Journal of Mathematical Analysis and Ap- cations, 2005(31): 495-505.

引证文献6

二级引证文献9

河南大学学报（自然科学版）
2010年 第5期

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