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<p>This research investigates the properties of fractional differential equations characterized by variable orders, focusing on their existence, uniqueness, and Ulam-Hyers stability. By transforming the problem into an integral equation format, we established essential conditions and utilized well-known fixed-point theorems to derive our results. The application of these mathematical strategies enables us to confirm the existence, uniqueness, and stability of solutions for the equations under consideration. Additionally, to highlight the practical implications of our findings, we present a specific example that effectively illustrates the core outcomes of this study.</p>

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Innovative approaches to initial and terminal value problems of fractional differential equations with two different derivative orders

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月6日

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  • Ahmed Refice,
  • M’hamed Bensaid,
  • Mohammed Said Souid,
  • Salah Boulaaras,
  • Abdelkader Amara,
  • Taha Radwan

摘要

This research investigates the properties of fractional differential equations characterized by variable orders, focusing on their existence, uniqueness, and Ulam-Hyers stability. By transforming the problem into an integral equation format, we established essential conditions and utilized well-known fixed-point theorems to derive our results. The application of these mathematical strategies enables us to confirm the existence, uniqueness, and stability of solutions for the equations under consideration. Additionally, to highlight the practical implications of our findings, we present a specific example that effectively illustrates the core outcomes of this study.