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<p>This research examines the existence and uniqueness of solutions for a system of pantograph fractional differential equations that incorporate the Caputo-Hadamard fractional derivative. The existence of solutions is verified through Schaefer’s fixed point theorem, and a well-established technique in functional analysis. Additionally, the uniqueness of solutions is proven using the Banach contraction mapping principle. To support these theoretical results, numerical examples are provided, illustrating and validating the findings. This study offers a comprehensive analysis of the mathematical properties of fractional differential equations, contributing valuable insights and fostering future developments in this field.</p>

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Applicability of Caputo-Hadmard fractional operator in mathematical modeling of pantograph systems

  • 期刊论文

  • 发表日期：

    2025年2月21日

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  • Muath Awadallah,
  • Mohamed Hannabou,
  • Hajer Zaway,
  • Jihan Alahmadi

摘要

This research examines the existence and uniqueness of solutions for a system of pantograph fractional differential equations that incorporate the Caputo-Hadamard fractional derivative. The existence of solutions is verified through Schaefer’s fixed point theorem, and a well-established technique in functional analysis. Additionally, the uniqueness of solutions is proven using the Banach contraction mapping principle. To support these theoretical results, numerical examples are provided, illustrating and validating the findings. This study offers a comprehensive analysis of the mathematical properties of fractional differential equations, contributing valuable insights and fostering future developments in this field.