| 模糊微分方程可约的条件 |
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| 引用本文： | 吉利业,尤翠莲.模糊微分方程可约的条件[J].河北大学学报(自然科学版),2020,40(4):337-343. |
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| 作者姓名： | 吉利业 尤翠莲 |
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| 作者单位： | 河北大学数学与信息科学学院,河北保定071002 |
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| 基金项目： | 国家自然科学基金资助项目(61773150);河北省教育厅重点基金资助项目(ZD2020172);河北省教育厅青年基金资助项目(QN2020124) |
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| 摘 要： | 模糊微分方程是在模糊环境下研究动态系统的重要工具,所以对方程进行求解是一项必不可少的工作.为了能使更多的模糊微分方程更容易求解,通过对非线性模糊微分方程进行变量替换判断方程是否可约,并在此过程中试图找到非线性模糊微分方程转化成线性模糊微分方程的方法.最后给出了2种形式的模糊微分方程是否可约的充分条件,同时推导出非线性模糊微分方程转化为线性模糊微分方程的具体方法,使可约模糊微分方程更容易辨别和求解,并且给出算例验证了结果的有效性.
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| 关 键 词： | 模糊变量 模糊过程 模糊积分 变量替换 可约模糊微分方程 |
| 收稿时间： | 2019-11-27 |
Reducibility conditions for fuzzy differential equation |
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| JI Liye,YOU Cuilian.Reducibility conditions for fuzzy differential equation[J].Journal of Hebei University (Natural Science Edition),2020,40(4):337-343. |
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| Authors: | JI Liye YOU Cuilian |
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| Institution: | College of Mathematics and Information Science, Hebei University, Baoding 071002, China |
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| Abstract: | Fuzzy differential equation is an important tool for studying dynamic system in fuzzy environment. Therefore, finding the solutions to these equations is essential. In order to make more fuzzy differential equations easier to solve, variables substitution is performed in nonlinear fuzzy differential equation to judge whether the equation is reducible. In this process, we try to find out the method to reduce a nonlinear fuzzy differential equation to a linear fuzzy differential equation. In the last, the conditions of two types of fuzzy differential equations being reducible are given. Therefore, it becomes easy to distinguish reducible fuzzy differential equations and solve them. In addition, some examples are given to verify the effectiveness of the results. |
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| Keywords: | fuzzy variable fuzzy process fuzzy integral variables substitution reducible fuzzy differential equation |
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