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分数阶微分方程积分边值问题解的存在性 被引量：2

Existence of Solutions to Integral Boundary Value Problems for the Fractional Differential Equation
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摘要 研究了带有积分边值条件的分数阶微分方程的边值问题,利用Banach压缩映像原理和Krasnoselskii不动点定理,得到了分数阶微分方程边值问题解的存在性、唯一性和至少存在一个解的充分条件. The existence of solutions to the integral boundary value problems for the fractional differential equations was studied by using Banach contraction principle and Krasnoselskii fixed point theorem.The sufficient conditions of existence,uniqueness of the solution and existence of at least one solution to the integral boundary value problem were obtained.
作者 章美月 刘文斌
机构地区 中国矿业大学理学院数学系
出处 《应用泛函分析学报》 CSCD 2013年第2期167-171,共5页 Acta Analysis Functionalis Applicata
基金 国家自然科学基金(11271364 51204163)
关键词 分数阶 积分边值问题 解 存在性 Banach压缩映像原理 KRASNOSELSKII不动点定理 fractional differential equations integral boundary value problem solutions existence Banach contraction principle Krasnoselskii fixed point theorem
分类号 O175.8 [理学—基础数学]
  • 相关文献

参考文献6

  • 1Kilbas A A,Srivastava H M,Trujillo J J. Theory and applications of fractional differential equations[M].North-Holl and Mathematics Studies,Amsterdam:Elsevier,2006.
  • 2Podlubny I. Fractional differential equations[M].New York:Academic Press,Inc,1993.
  • 3Jiang D Q,Yuan C J. The positive properties of the Green function for Dirichlet type boundary value problems of nonlinear fractional differential equations and its application[J].Nonlinear Analysis-Theory Methods and Applications,2010,(72):710-719.
  • 4Bal Z B,Lu H S. Positive solutions for boundary value problem of nonlinear fractional differential equation[J].Journal of Mathematical Analysis and Applications,2005,(31):495-505.
  • 5Xu X J,Jiang D Q,Yuan C J. Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation[J].Nonlinear Analysis-Theory Methods and Applications,2009,(71):4676-4688.
  • 6华守亮,吕志伟.分数阶微分方程边值问题解的存在性及唯一性[J].河南大学学报（自然科学版）,2010,40(5):453-455. 被引量：6

二级参考文献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.

共引文献5

同被引文献7

  • 1Kilbas 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.
  • 2Podlubny I. Factional Differential Equations[M]. New York: Academic Press, 1993.
  • 3Jiang 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.
  • 4Bai 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.
  • 5Xu X J, Jiang D (Qa, Yuan C J. Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation[J]. Nonlinear Analysis, 2009(71): 4676-4688.
  • 6华守亮,吕志伟.分数阶微分方程边值问题解的存在性及唯一性[J].河南大学学报（自然科学版）,2010,40(5):453-455. 被引量：6
  • 7张立新,王海菊.含积分边界条件的分数阶微分方程边值问题的正解的存在性[J].纯粹数学与应用数学,2013,29(5):450-457. 被引量：7

引证文献2

应用泛函分析学报
2013年 第2期

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