Scholarlink

<p>The generalized derivative represents the broadest notion of the Hukuhara-type derivative of a fuzzy number-valued function in the literature. It exists for a wide class of fuzzy processes, since the generalized difference exists for any pair of fuzzy numbers. Despite its historical significance, few papers provide theoretical results on the g-derivative, primarily because of its complex analytical behavior. On the other hand, analyzing solutions to fuzzy differential equations from a comparative Hukuhara-type perspective allows establishing features of FDEs whose solutions are exclusively g-differentiable. The study begins by providing a corrected version of the fundamental theorem of calculus via the g-differentiability and Aumann integrability of a fuzzy function. Sufficient conditions over the field of a fuzzy initial value problem for the gH<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(*\)</EquationSource> </InlineEquation>-differentiability of the solutions are presented. Lastly, results on fuzzy processes derived from solutions of FDEs that are g-differentiable, but not gH, and not even gH<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(*\)</EquationSource> </InlineEquation>-differentiable, are given. Examples of population dynamics governed by the Malthusian and Logistic models are provided to illustrate different scenarios for the presented analysis.</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

Analysis of solutions of fuzzy differential equations under the generalized derivative

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年2月11日

查看全文
  • Felipe Longo,
  • Beatriz Laiate,
  • Marta C. Gadotti,
  • João F. C. A. Meyer

摘要

The generalized derivative represents the broadest notion of the Hukuhara-type derivative of a fuzzy number-valued function in the literature. It exists for a wide class of fuzzy processes, since the generalized difference exists for any pair of fuzzy numbers. Despite its historical significance, few papers provide theoretical results on the g-derivative, primarily because of its complex analytical behavior. On the other hand, analyzing solutions to fuzzy differential equations from a comparative Hukuhara-type perspective allows establishing features of FDEs whose solutions are exclusively g-differentiable. The study begins by providing a corrected version of the fundamental theorem of calculus via the g-differentiability and Aumann integrability of a fuzzy function. Sufficient conditions over the field of a fuzzy initial value problem for the gH \(*\) -differentiability of the solutions are presented. Lastly, results on fuzzy processes derived from solutions of FDEs that are g-differentiable, but not gH, and not even gH \(*\) -differentiable, are given. Examples of population dynamics governed by the Malthusian and Logistic models are provided to illustrate different scenarios for the presented analysis.