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<p>This paper investigates the existence and uniqueness of solutions (EUSS) for a finite delayed problem of fractional differential equations with nonlinear variable order (FDPFDENVO). The analysis employs advanced mathematical tools, including the schauder fixed-point theorem (SFPT) and the banach fixed-point theorem (BFPT), offering a streamlined approach that requires fewer restrictive assumptions. To demonstrate the practical relevance of the theoretical findings, the study includes an applied example. The results hold significant value for understanding complex dynamical systems with time delays, with potential applications in engineering, economics, and medicine. Additionally, the findings contribute to refining numerical methods for solving delay equations.</p>

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On the Finite Delayed Fractional Differential Equation via Riemann–Liouville Derivative of Non-linear Variable-Order

  • 期刊论文

  • 发表日期：

    2025年8月31日

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  • Mohammed Said Souid,
  • Hatıra Günerhan,
  • Hallouz Abdelhamid,
  • Hemen Dutta

摘要

This paper investigates the existence and uniqueness of solutions (EUSS) for a finite delayed problem of fractional differential equations with nonlinear variable order (FDPFDENVO). The analysis employs advanced mathematical tools, including the schauder fixed-point theorem (SFPT) and the banach fixed-point theorem (BFPT), offering a streamlined approach that requires fewer restrictive assumptions. To demonstrate the practical relevance of the theoretical findings, the study includes an applied example. The results hold significant value for understanding complex dynamical systems with time delays, with potential applications in engineering, economics, and medicine. Additionally, the findings contribute to refining numerical methods for solving delay equations.