Scholarlink

<p>The fuzzy Henstock integral provides a flexible and powerful tool for handling high oscillation functions, its primitive is a fuzzy bounded variation function rather than a fuzzy absolutely continuous function. In this paper, we first provide some basic properties of fuzzy bounded variation function spaces. Then it was proved that the solution of the generalized fuzzy differential equations(GFDEs) based on fuzzy Henstock integral must be a bounded variation function, which is to give the structure for the bounded variation solutions(BV-solutions) of the GFDEs. Finally, by using the embedding theorem for fuzzy number space and Schauder Tichonov’s fixed point theorem, we obtain the existence theorem of BV-solutions for GFDEs. In addition, we provide the local uniqueness theorems for two types of fuzzy solutions of GFDEs.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On bounded variation solutions of generalized fuzzy differential equations

  • 期刊论文

  • 发表日期：

    2025年8月19日

查看全文
  • Yang Li,
  • Yabin Shao

摘要

The fuzzy Henstock integral provides a flexible and powerful tool for handling high oscillation functions, its primitive is a fuzzy bounded variation function rather than a fuzzy absolutely continuous function. In this paper, we first provide some basic properties of fuzzy bounded variation function spaces. Then it was proved that the solution of the generalized fuzzy differential equations(GFDEs) based on fuzzy Henstock integral must be a bounded variation function, which is to give the structure for the bounded variation solutions(BV-solutions) of the GFDEs. Finally, by using the embedding theorem for fuzzy number space and Schauder Tichonov’s fixed point theorem, we obtain the existence theorem of BV-solutions for GFDEs. In addition, we provide the local uniqueness theorems for two types of fuzzy solutions of GFDEs.