中山大学学报自然科学版 ›› 2016, Vol. 55 ›› Issue (2): 1-6.doi: 10.13471/j.cnki.acta.snus.2016.02.001

• 研究论文 •    下一篇

一类非线性分数阶差分方程边值问题解的存在性及Ulam稳定性

王金华1,向红军1, 赵育林2   

  1. 1.湘南学院数学与金融学院,湖南 郴州 423000;
    2.中山大学数学与计算科学学院,广东 广州 510275
  • 收稿日期:2015-12-10 出版日期:2016-03-25 发布日期:2016-03-25
  • 通讯作者: 向红军;E-mail:hunxhjxhj67@126.com

Existence and Ulam stability of solutions for a boundary value problem of nonlinear fractional difference equation

WANG Jinhua1, XIANG Hongjun1, ZHAO Yulin2   

  1. 1.College of Mathematics and Finance, Xiangnan University, Chenzhou 423000, China;
    2. School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275, China
  • Received:2015-12-10 Online:2016-03-25 Published:2016-03-25

摘要:

讨论了一类非线性分数阶差分方程解的存在性及Ulam稳定性。应用Schaefer不动点定理及不等式技巧获得了方程解的存在性结果,同时得到了方程的解具有Ulam稳定性的新判据,并举例说明了所得主要结果的有效性。

关键词: 分数阶差分方程, 不动点, 存在性, Ulam稳定性

Abstract:

The existence and Ulam stability of solutions of a discrete nonlinear fractional boundary value problem are studied. The existence results are established based on Schaefer fixed point theorem and inequality analysis technique. Meanwhile, new criteria for Ulam stability of solutions to the nonlinear fractional difference equation are provided and examples are presented to illustrate the effectiveness of the main results.

Key words: fractional difference equation, fixed point, existence, Ulam stability

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