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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报

• • 上一篇    下一篇

带有非奇异核分数阶差分方程的比较原理及解的不确定性分布

陈雨婷,   李晓艳,   王雪芹   

  1. 安徽大学数学科学学院，合肥 230601
  • 出版日期:2022-12-15 发布日期:2022-12-15
  • 通讯作者: 李晓艳 E-mail: lxynnfjl@126.com
  • 基金资助:
    安徽省高校自然科学研究项目 (KJ2019A0004).

A Comparison Theorem and the Uncertainty Distribution of Solutions for Fractional Difference Equations with Nonsingular Kernel

CHEN Yuting,   LI Xiaoyan,   WANG Xueqin   

  1. School of Mathematical Sciences, Anhui University, Hefei 230601
  • Online:2022-12-15 Published:2022-12-15
  • Contact: X. Li. E-mail address: lxynnfjl@126.com
  • Supported by:
    The College Natural Science Research Project of Anhui Province (KJ2019A0004).

PDF (PC)

523

摘要：

比较原理对于研究分数阶方程的性质具有重要的作用。首先，证明了 ABR 型分数阶差分方程的比较原理。其次，利用比较原理，建立了不确定性分数阶差分方程的解与其 $\alpha$-路径之间的联系。接着，给出了 ABR 型不确定性分数阶差分方程解的不确定性分布。最后，具体的实例验证了主要结论的正确性。

关键词: ABR 型分数阶差分方程, 比较原理, 不确定分布, $\alpha$-路径

Abstract:

Comparison theorems play an essential role in studying the properties of the fractional equations. Firstly, a comparison theorem for ABR type fractional difference equations is proved. Next, based on the proven comparison theorem, the connections between the solution for an uncertainty fractional difference equation and its $\alpha$-path are established. Then, the uncertainty distribution of solutions for ABR type uncertainty fractional difference equations is also derived. Finally, examples are given to verify the correctness of main results.

Key words: ABR type fractional difference equations, comparison theorem, uncertainty distribution, $\alpha$-path

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