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<p>This study delves into the existence, uniqueness, and stability of solutions for a nonlinear coupled system incorporating mixed generalized fractional derivatives. The system is characterized by <i>ψ</i>-Caputo and <i>ϕ</i>-Riemann-Liouville fractional derivatives with mixed boundary conditions. We provide essential preliminaries and definitions, followed by a detailed analysis using fixed point theory to establish the main results. Furthermore, we discuss the Hyers-Ulam stability of the proposed system and illustrate the theoretical findings with several examples. This study extends and generalizes various results in the literature and provides new insights into the qualitative behavior of fractional differential systems.</p>

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Existence, uniqueness and stability analysis of a nonlinear coupled system involving mixed ϕ-Riemann-Liouville and ψ-Caputo fractional derivatives

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年1月17日

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  • Said Zibar,
  • Brahim Tellab,
  • Abdelkader Amara,
  • Homan Emadifar,
  • Atul Kumar,
  • Sabir Widatalla

摘要

This study delves into the existence, uniqueness, and stability of solutions for a nonlinear coupled system incorporating mixed generalized fractional derivatives. The system is characterized by ψ-Caputo and ϕ-Riemann-Liouville fractional derivatives with mixed boundary conditions. We provide essential preliminaries and definitions, followed by a detailed analysis using fixed point theory to establish the main results. Furthermore, we discuss the Hyers-Ulam stability of the proposed system and illustrate the theoretical findings with several examples. This study extends and generalizes various results in the literature and provides new insights into the qualitative behavior of fractional differential systems.