一类高阶模糊微分方程的Hyers-Ulam稳定性  

On the Hyers-Ulam stability fora class of higher order fuzzy differential equations

作　　者：郭元伟[1] 邵亚斌 GUO Yuan-wei;SHAO Ya-bin(Department of Mathematics,Taiyuan Institute,Taiyuan 030032,Shanxi,China;College of Science,Chongqing University of Posts and Telecommunications,Chongqing 400065,China)

机构地区：[1]太原学院数学系,山西太原030032 [2]重庆邮电大学理学院,重庆400065

出　　处：《西北师范大学学报（自然科学版）》2023年第1期47-55,共9页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(61806030,61876201);山西省高等学校科技创新项目(2022L581);太原学院校级一般科研项目(21TYKY03)。

摘　　要：在新的广义模糊距离意义下,证明了一类高阶模糊连续函数空间的完备性;结合强广义微分和高阶模糊连续函数空间中的不动点定理,讨论了二阶微分方程x″(t)=f(t,x(t),x′(t))和高阶微分方程x^((n))(t)=f(t,x(t),…,x^((n-1))(t))的Hyers-Ulam-Rassias稳定性和Hyers-Ulam稳定性,并针对二阶模糊微分方程,给出了具体的算例.The completeness for a class of higher order fuzzy continuous function space is proved in a new generalized fuzzy distance sense.Under strong generalized differentiability,the Hyers-Ulam-Rassias stability and Hyers-Ulam stability forthe fuzzy differential equations x″(t)=f(t,x(t),x′(t))and x^((n))(t)=f(t,x(t),…,x^((n-1))(t))are studied by employing the fixed point technique.In addition,two examples are given to verify these results for the second order fuzzy differential equation.

关 键 词：强广义微分 模糊微分方程 HYERS-ULAM-RASSIAS稳定性 HYERS-ULAM稳定性 

分 类 号：O159[理学—数学]