| 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 |
| |
| 引用本文： | 陈雨婷,李晓艳,王雪芹.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[J].工程数学学报,2022,39(6):910-924. |
| |
| 作者姓名： | 陈雨婷 李晓艳 王雪芹 |
| |
| 作者单位： | 安徽大学数学科学学院，合肥 230601 |
| |
| 基金项目： | 安徽省高校自然科学研究项目 (KJ2019A0004). |
| |
| 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 |
A Comparison Theorem and the Uncertainty Distribution of Solutions for Fractional Difference Equations with Nonsingular Kernel |
| |
| CHEN Yuting,LI Xiaoyan,WANG Xueqin.A Comparison Theorem and the Uncertainty Distribution of Solutions for Fractional Difference Equations with Nonsingular Kernel[J].Chinese Journal of Engineering Mathematics,2022,39(6):910-924. |
| |
| Authors: | CHEN Yuting LI Xiaoyan WANG Xueqin |
| |
| Affiliation: | School of Mathematical Sciences, Anhui University, Hefei 230601 |
| |
| 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. |
| |
| Keywords: | ABR type fractional difference equations comparison theorem uncertainty distribution $\alpha$-path |
|
| 点击此处可从《工程数学学报》浏览原始摘要信息 |
|
点击此处可从《工程数学学报》下载全文 |
