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一类分数阶微分方程系统边值问题正解的存在性 被引量：1

Existence of Positive Solutions for Boundary Value Problem of a Coupled System of Nonlinear Fractional Differential Equations
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摘要 利用锥拉伸与压缩不动点定理和Leray-Schauder非线性抉择,讨论了一类非线性的Riemann-Liouville分数阶微分方程耦合系统边值问题,得出边值问题的正解存在的充分条件. In this paper, the existence of positive solutions for boundary value problem of a coupled system of nonlinear fractional differential equations was discussed. By using the fixed-point theorems, some results were obtained.
作者 申腾飞 宋文耀
机构地区 中国矿业大学理学院
出处 《常熟理工学院学报》 2012年第4期28-34,共7页 Journal of Changshu Institute of Technology
关键词 分数阶微分方程 边值问题 不动点定理 正解 Fractional differential equation boundary value problem fixed point theorem positive solution
分类号 O175.8 [理学—基础数学]
  • 相关文献

参考文献11

  • 1Kilbas A A, Srivastava H M, Trujillo J J. Theory and Applications of Fractional Differentia[ Equations[M]. Amsterdam: Elsevier, 2006.
  • 2Xinwei Su. Boundary value problem for a coupled system of nonlinear fractional differential equations[J]. Appl Math Lett, 2009, 22 : 64-69.
  • 3Zhanbing Bai, Haishen Lv. Positive solutions for boundary value problem of nonlinear fractional differential equation[J]. J Math Anal Appl, 2005, 311(2): 495-505.
  • 4Bashir Ahmad, Juan J Nieto. Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions[J]. Comput Math Appl, 2009, 58: 1838-1843.
  • 5Hongrui Sun, Lutian Tang, Yinghai Wang. Eigenvalue problem for p-Laplacain three-point boundary value problems on time scales [J]. J Math Anal Appl, 2007, 331: 248-262.
  • 6Shuqin Zhang. Positive solutions for boundary value problems of nonlinear fractional differential equations[J]. Electronic Journal of Differential Equations, 2006(36): 1-12.
  • 7Gan S Q. Dissipativity of 0 -methods for Nonlinear Volterra Delay-integro-differential Equations[J]. J Comput Appl Math, 2007, 206: 98-- 907.
  • 8Shuqin Zhang. Existence of positive solution for some class of nonlinear fractional differential equations[J]. J Math Anal Appl, 2003, 278: 136-148.
  • 9Xiaojie Xu, Daqing Jang. Multiple positive solutions for the boundary value Problem of a nonlinear fractional differential equation[J]. Nonlinear Analysis, 2009, 71: 4676-4688.
  • 10Zhanbing Bai. On positive solutions of a nonloeal fractional boundary value problem[J]. Nonlinear Analysis, 2010, 72: 916-924.

二级参考文献5

  • 1Bai Z B, Lii H S. Positive solutions for boundary value problem of nonlinear fractional differential equa- tion[J]. J Math Anal Appl, 2005, 311:495-505.
  • 2Zhang S Q. Positive solutions for boundary-value problems of nonlinear fractional differential equations[J]. Electronic Journal of Differential Equations, 2006, 36:1-12.
  • 3Gejji V D, Jafari H. Adomian decomposition: a tool for solving a system of fractional differential equa- tions[J]. J Math Anal Appl, 2005, 301:508-518.
  • 4Podlubny I. Fractional Differential Equations, Mathematics in Science and Engineering[M]. New York/London/Toronto: Academic Press, 1999. vol, 198.
  • 5Samko S G, Kilbas A A, Marichev O I. Fractional Integrals and Derivatives (Theory and Applications)[M]. Switzerland: Gordon and Breach, 1993.

共引文献29

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常熟理工学院学报
2012年 第4期

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