Scholarlink

<p>This study investigates the existence and uniqueness of solutions for a coupled system of Langevin-type fractional differential equations featuring generalized Ψ-Caputo derivatives in arbitrary Banach spaces. While prior research has predominantly focused on finite-dimensional or specific function spaces, this work extends the framework to infinite-dimensional settings, offering a more versatile analytical approach. Uniqueness is established using Banach’s fixed-point theorem under Lipschitz-type conditions, while existence is proven via Monch’s fixed-point principle combined with the measure of noncompactness—a powerful tool for infinite-dimensional problems. Demonstrative examples, including cases in the space of null sequences, validate the theoretical framework. The findings enhance the study of fractional coupled systems, introducing a flexible and comprehensive approach that integrates diverse fractional operators and strengthens foundational results.</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

A coupled system of Langevin-type fractional differential equations involving Ψ-Caputo derivatives in arbitrary Banach spaces

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年5月4日

查看全文
  • Abdelkader Moumen,
  • Oualid Zentar,
  • Jehad Alzabut,
  • Hicham Saber,
  • Tariq Alraqad

摘要

This study investigates the existence and uniqueness of solutions for a coupled system of Langevin-type fractional differential equations featuring generalized Ψ-Caputo derivatives in arbitrary Banach spaces. While prior research has predominantly focused on finite-dimensional or specific function spaces, this work extends the framework to infinite-dimensional settings, offering a more versatile analytical approach. Uniqueness is established using Banach’s fixed-point theorem under Lipschitz-type conditions, while existence is proven via Monch’s fixed-point principle combined with the measure of noncompactness—a powerful tool for infinite-dimensional problems. Demonstrative examples, including cases in the space of null sequences, validate the theoretical framework. The findings enhance the study of fractional coupled systems, introducing a flexible and comprehensive approach that integrates diverse fractional operators and strengthens foundational results.