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一类带有分数阶非局部边值条件的分数阶差分方程解的存在性 被引量：3

Existence of Solutions for a Class of Fractional Difference Equation with Nonlocal Fractional Boundary Conditions
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摘要 研究了一类带有非局部分数阶边值条件的分数阶差分方程解的存在性与唯一性.首先给出了这个问题解的表达式,然后分析了格林函数的一些性质,并运用压缩映像原理,Brouwer定理以及Krasnoselskii定理证明了该问题解的存在唯一性.所得结论推广了现有文献中的一些结果,并给出了具体例子用以说明文中的主要结论. We study the existence and uniqueness of solution for a class of fractional difference equation with nonlocal fractional boundary conditions. Firstly we give a representation for the solution to this problem. Then, we analysis some properties of the Green＇s function and prove the existence and uniqueness of solution by using the contraction mapping theorem, the Brouwer theorem, and the Krasnosel＇skii theorem. The results extend and improve the results given in literatures. An example is given to illustrate our main results.
作者 慎闯 何延生
机构地区 延边大学数学系
出处 《烟台大学学报（自然科学与工程版）》 CAS 2013年第2期90-96,共7页 Journal of Yantai University(Natural Science and Engineering Edition)
基金 国家自然科学基金资助项目(11161049)
关键词 分数阶差分方程 边值问题 非局部条件 解的存在唯一性 fractional difference equation boundary value problem nonlocal conditions existence and uniqueness of solution
分类号 O175 [理学—基础数学]
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参考文献12

  • 1Kilbas A A, Srivastava H M, Trujillo J J. Theory and Applications of Fractional Differential Equations [ M ]. Amsterdam : North- Holland Mathematics Studies,2006.
  • 2Miller K S, Ross B. An Introuction to the Fractional Calculus and Differential Equations [ M ]. New York : Wileg-Interscience, 1933.
  • 3Oldham K B, Spanier J. The Fractional Calculus [ M 1. New York : Academic Press, 1974.
  • 4Atici F M, Eloe P W. Two-point boundary value problems for finite fractional difference equations [ J ]. Difference Equations Ap- plications, 2010,17 ( 4 ) 445 -456.
  • 5Goodrich C S. Solutions to a discrete right-focal fractional boundary value problem[ J ]. Difference Equations,2010,5 (2) :195- 216.
  • 6Cheung W, Ren J, Wong P J Y, D. Multiple positive solutions for discrete nonlocal boundary value problems [ J ]. Mathematical Analysis and Applications ,2007,330 (2) :900-915.
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  • 8Goodrich Christopher S. Existence and uniqueness of solutions to a fractional difference equationwith nonlocal conditions [ J ]. Computers Mathematics with Applications ,2011,61 (2) : 191-202.
  • 9Atici F M, Eloe P W. Initial value problems in discrete fractional calculus [ J]. Proceedings of the American Mathematical Soci- ety, 2009,137 ( 3 ) : 981-989.
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同被引文献21

  • 1Goodrich C S.Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions[J].J.Comput.Math.Appl,2011,61(2):191-202.
  • 2Goodrich C S.On a fractional boundary value problem with fractional boundary conditions[J].Appl Math Lett,2012,25(8):1101-1105.
  • 3Goodrich C S.Solutions to a discrete right-focal boundary value problem[J].Int.J.Difference Equ,2010,5(2):195-216.
  • 4Atici F M,engül S.Modeling with fractional difference equations[J].J.Math.Anal.Appl,2010,369(1):1-9.
  • 5Goodrich C S.On discrete sequential fractional boundary value problems[J].J.Math.Anal.Appl,2012,385(1):111-124.
  • 6Goodrich C S.Existence of a positive solution to a system of discrete fractional boundary value problems[J].J.Applied Mathematics and Computation,2011,217(9):4740-4753.
  • 7Chen Fulai,Luo Xiannan,Zhou Yong.Existence results for nonlinear fractional difference equation[J].J.Advances in Difference Equations,2011,2011(1):1-12.
  • 8Goodrich C S.Existence of a positive solution to a system of discrete fractional boundary value problems[J].Comput.Math.Appl.2011,217(9):4740-4753.
  • 9Huang Zhongmin,Hou Chengmin.Solvability of nonlocal fractional boundary value problems[J].Discrete Dynamics in Nature and Society,2013,2013(1):1-9.
  • 10Kang Shugui,Li Yan,Chen Huiqin.Positive solutions to boundary value problems of fractional difference equation with nonlocal conditions[J].Advances in Difference Equations,2014(1):1-12.

引证文献3

二级引证文献4

烟台大学学报（自然科学与工程版）
2013年 第2期

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