隐式分数阶模糊微分方程初值问题解的唯一性

doi:10.6040/j.issn.1671-9352.0.2021.325

《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (4): 85-90.doi: 10.6040/j.issn.1671-9352.0.2021.325

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隐式分数阶模糊微分方程初值问题解的唯一性

席艳丽,陈鹏玉^*

西北师范大学数学与统计学院, 甘肃兰州 730070

发布日期:2022-03-29
作者简介:席艳丽(1997— ),女,硕士研究生,研究方向为非线性泛函分析及其应用. E-mail:XYL9702@163.com*通信作者简介:陈鹏玉(1986— ),男,博士,副教授,硕士生导师,研究方向为非线性泛函分析及其应用. E-mail:chpengyu123@163.com
基金资助:
国家自然科学基金资助项目(12061063);西北师范大学青年教师科研能力提升计划资助项目(NWNU-LKQN2019-3);西北师范大学参与式研讨课教学改革项目

Uniqueness of solutions for initial value problems of implicit fractional order fuzzy differential equations

XI Yan-li, CHEN Peng-yu^*

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China

Published:2022-03-29

摘要/Abstract

摘要： 运用幂压缩映射原理,研究了隐式分数阶模糊微分方程初值问题{^CD^α,p_a⁺u(t)=f(t,u(t), ^CD^α,p_a⁺u(t)),u(a)=u₀解的唯一性,其中 00 是给定的实数,^CD^α,p_a⁺ 是模糊Caputo-Katugampola分数阶广义Hukuhara导数, f:［a,b］×E×E→E是一个模糊函数,E是模糊空间。

关键词: Caputo-Katugampola 分数阶导数, 初值问题, 幂压缩映射原理, 分数阶模糊微分方程

Abstract: By using the principle of power compression mapping, this paper obtains the uniqueness of solution to the initial value problems of implicit fractional fuzzy differential equations{^CD^α,p_a⁺u(t)=f(t,u(t), ^CD^α,p_a⁺u(t)),u(a)=u₀,where 00,1), p>0 is a fixed real number, and CDα,p_a⁺ is the fuzzy Caputo-Katugampola fractional generalized Hukuhara derivative, f:［a,b］×E×E→E is a fuzzy function. E is the fuzzy space.

Key words: Caputo-Katugampola fractional derivative, initial value problem, power compression mapping principle, fractional fuzzy differential equations

中图分类号:

O175.14

引用本文

席艳丽,陈鹏玉. 隐式分数阶模糊微分方程初值问题解的唯一性[J]. 《山东大学学报(理学版)》, 2022, 57(4): 85-90.

XI Yan-li, CHEN Peng-yu. Uniqueness of solutions for initial value problems of implicit fractional order fuzzy differential equations[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(4): 85-90.

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[1] 安佳辉,陈鹏玉. 变分数阶微分方程初值问题解的存在性[J]. 《山东大学学报(理学版)》, 2020, 55(6): 41-47.

[2] 李娇. Caputo分数阶微分方程初值问题解的存在性与惟一性[J]. J4, 2013, 48(4): 60-64.

[3] 王建国,刘春晗. Banach空间积-微分方程含间断项边值问题的解[J]. J4, 2013, 48(10): 18-22.

[4] 李耀红1,2,张海燕1. Banach空间中二阶非线性混合型积分-微分方程初值问题的解[J]. J4, 2010, 45(12): 93-97.

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[1]	安佳辉,陈鹏玉. 变分数阶微分方程初值问题解的存在性[J]. 《山东大学学报(理学版)》, 2020, 55(6): 41-47.
[2]	李娇. Caputo分数阶微分方程初值问题解的存在性与惟一性[J]. J4, 2013, 48(4): 60-64.
[3]	王建国,刘春晗. Banach空间积-微分方程含间断项边值问题的解[J]. J4, 2013, 48(10): 18-22.
[4]	李耀红1,2,张海燕1. Banach空间中二阶非线性混合型积分-微分方程初值问题的解[J]. J4, 2010, 45(12): 93-97.

隐式分数阶模糊微分方程初值问题解的唯一性

Uniqueness of solutions for initial value problems of implicit fractional order fuzzy differential equations

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