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山东大学学报（理学版） ›› 2017, Vol. 52 ›› Issue (10): 42-49.doi: 10.6040/j.issn.1671-9352.0.2016.594

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一类模糊积分微分方程的模糊微分变换法

张琬迪,宋晓秋*,吴尚伟   

  1. 中国矿业大学数学学院, 江苏 徐州 221116
  • 收稿日期:2016-11-25 出版日期:2017-10-20 发布日期:2017-10-12
  • 通讯作者: 宋晓秋(1963— ),男,教授,研究方向为应用泛函分析和模糊数学原理及其应用.E-mail:songxiaoqiu668@163.com E-mail:zhangwandixf@163.com
  • 作者简介:张琬迪(1992— ),女,硕士研究生,研究方向为模糊数学原理及其应用.E-mail:zhangwandixf@163.com
  • 基金资助:
    国家自然科学基金资助项目(51374199)

Application of fuzzy differential transform method for solving fuzzy integral differential equation

  1. School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China
  • Received:2016-11-25 Online:2017-10-20 Published:2017-10-12

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摘要： 根据模糊数相关知识和模糊微分变换的定义,给出了一阶导数f '(x)与f(x)对应的模糊微分变换函数之间的关系,以及二重积分函数f(x)与被积函数u(x)和g(x)对应的模糊微分变换函数F(k)和U(k)与G(k)之间的关系,进而给出求解模糊积分微分方程的相关结果。

关键词: 模糊微分变换, 模糊数, 模糊积分微分方程, FDTM, H-导数

Abstract: According to the definitions of fuzzy number and fuzzy differential transformation, the relationship between the differential transform of the functions f '(x) and f(x)is given, and the relationship between F(k), U(k) and G(k), the differential transform of double function f(x), integrand u(x)and g(x), is given, then the solution of fuzzy integral differential equation is obtained.

Key words: fuzzy differential transform, FDTM, H-derivative, fuzzy number, fuzzy integral differential equation

中图分类号: 

  • O159
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