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Banach空间中一类分数阶微分方程边值问题 被引量：6

Boundary value problem for a class of fractional differential equations in Banach spaces
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摘要 研究Banach空间中一类非线性分数阶微分方程边值问题.构建此类方程的Green函数,利用非紧测度和相关的不动点定理,得到了此类方程的mild解存在的几个充分条件,所得结果改进和推广了一些已有的结论. This paper is concerned with a class of nonlinear differential equations with boundary value conditions in Banach spaces. By using the Green＇s function, theory of measure of noncompactness and fixed point theorem, existence results of mild solutions are obtained, which improve and generalize some previous results.
作者 董琪翔 毋光先 李姣
机构地区 扬州大学数学科学学院 焦作师范高等专科学校数学系
出处 《纯粹数学与应用数学》 CSCD 2013年第1期1-10,共10页 Pure and Applied Mathematics
基金 国家自然科学基金(10971182) 江苏省自然科学基金(BK2009179 BK2010309) 江苏省高校自然科学基金(09KJB110010)
关键词 分数阶积分 分数阶导数 微分方程 边值问题 MILD解 fractional order integral, fractional order derivative, differential equation, boundary value problem,mild solution
分类号 O175.15 [理学—基础数学]
  • 相关文献

参考文献11

  • 1Rashid M H M,Al-Omari A. Local and global existence of mild solutions for impulsive fractional semilinear integro-differential equation[J].Commun Nonlinear Sci Nuner Simulat,2011.3493-3503.
  • 2Diethelm K. The Analysis of Fractional Differential Equations[M].{H}Berlin:Springer-Verlag,2010.
  • 3Kaufmann E R,Yao K D. Existence of solutions for a nonlinear fractional order differential equation[J].Electronic J Diff Quali Theory Equati,2009.1-9.
  • 4Bazhlekova E. Fractional Evolution Equations in Banach Space[D].Eindhoven:University Press Facilities Eindhoven University of Technology,2001.
  • 5Lakshmikantham V,Vatsala A S. Basic theory of fractional differentional equation[J].Nonlinear Anal,2008.2677-2682.
  • 6Zhang Shuqin. The existence of a positive solution for a nonlinear fractional differential equation[J].{H}Journal of Mathematical Analysis and Applications,2000.804-812.
  • 7卢芳,周宗福.一类分数阶微分方程边值问题正解的存在性[J].纯粹数学与应用数学,2011,27(5):672-678. 被引量：5
  • 8郭大钧.非线性分析中的半序方法[M]{H}济南:山东科学技术出版社,2000.
  • 9Dong Qixiang,Li Gang. Existence of solutions for semilinear differential equations with nonlocal conditions in Banach space[J].Electronic J Quali Theory Diff Equati,2009.1-13.
  • 10Dong Qixiang,Fan Zhenbin,Li Gang. Existence of solutions to nonlocal functional differential integrodif-ferential equations[J].Int J Nonlinear Sci,2008,(02):140-151.

二级参考文献4

  • 1Bai Zhanbing, Im Haishen. Positive solutions for boundary value problem of nonlinear fractional ditIierential equal, ion[J]. Math. Anal. Appl., 205,311:495-505.
  • 2Liang Sihua, Zhang Jihui. Positive solutions for boundary value problem of nonlinear fractional differential equation[J]. Nonlinear Analysis, 2009,71:5545-5550.
  • 3Meral F C, Royston T J, Magin R. Fractional calculus in viscoelasticity: an experimental study[J].Commuzl Nonlinear. Sci. Numer. Sirrml., 2010,15(4):939-945.
  • 4lAang S, Zhang J. Positive solutions for boundary value problem of nonlinear fractional differential equation[J1. Nonlinear Anal., 2009,71:5545-5550.

共引文献4

同被引文献35

  • 1Xiaogang Liu,Zigen Ouyang,Jichao Zhong.EXISTENCE AND UNIQUENESS OF SOLUTIONS TO A NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION[J].Annals of Differential Equations,2011,27(1):19-27. 被引量：3
  • 2张淑琴.EXISTENCE OF SOLUTION FOR A BOUNDARY VALUE PROBLEM OF FRACTIONAL ORDER[J].Acta Mathematica Scientia,2006,26(2):220-228. 被引量：27
  • 3郭大钧.非线性分析中的半序方法[M].济南：山东科技出版社,2000..
  • 4RASHID M H M, AL-OMARI A. Local and global existence of mild solutions for impulsive fractional semilinear integro-differential equation [J]. Commun Nonlinear Sci Nuner Simulat, 2011, 16(9): 3493-3503.
  • 5DIETHELM K. The analysis of fractional differential equations: an application-oriented exposition using differ- ential operators of Caputo type [M]. Berlin: Springer, 2010: 13-65.
  • 6ZHOU Wenxue, PENG Jigen. Existence of solutions to boundary value problem for fractional differential equa- tion [J]. Chin J Eng Math, 2011, 28(6) : 727-735.
  • 7BAJLEKOVA E G. Fractional evolution equations in Banach space [M]. Eindhoven: University Press Facilities, 2001: 1-18.
  • 8LAKSHMIKANTHAM V, VATSALA A S. Basic theory of fractional differentional equation [J]. Nonlinear Anal: Theor Meth Appl, 2008, 69(8): 2677-2682.
  • 9ZHANG Shuqin. The existence of a positive solution for a nonlinear fractional differential equation [J]. J Math Anal Appl, 2000, 252(2): 804-812.
  • 10DONG Qixiang, LI Gang. Existence of solutions for semilinear differential equations with nonlocal conditions in Banach space [J]. Electr J Quali Theory Diff Equati, 2009, 47: 1-13.

引证文献6

二级引证文献7

纯粹数学与应用数学
2013年 第1期

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