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<p>This article focuses on the analysis and numerical treatment of fractional neutral pantograph nonlocal system governed by the Atangana-Baleanu-Caputo (ABC) fractional derivative, which features a non-singular and non-local kernel. We establish sufficient conditions for the existence and uniqueness of mild solutions by applying semigroup theory and fixed-point techniques tailored to the structure of neutral-type functional differential equations with proportional delays. The analysis carefully handles the challenges posed by the non-local nature of the ABC derivative and the scale-invariant characteristics of pantograph terms. Furthermore, a concrete numerical example is provided using the Picard iteration method to demonstrate the feasibility, accuracy and effectiveness of the proposed theoretical framework. This validates the applicability of the approach to a class of memory-dependent dynamical systems with complex delay structures.</p>

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Fractional Neutral Pantograph Systems with Non-Singular Kernel: Analysis and Numerical Approximation

  • 期刊论文

  • 发表日期：

    2025年9月2日

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  • Yong-Ki Ma,
  • K. Jothimani,
  • N. Valliammal,
  • V. Vijayakumar

摘要

This article focuses on the analysis and numerical treatment of fractional neutral pantograph nonlocal system governed by the Atangana-Baleanu-Caputo (ABC) fractional derivative, which features a non-singular and non-local kernel. We establish sufficient conditions for the existence and uniqueness of mild solutions by applying semigroup theory and fixed-point techniques tailored to the structure of neutral-type functional differential equations with proportional delays. The analysis carefully handles the challenges posed by the non-local nature of the ABC derivative and the scale-invariant characteristics of pantograph terms. Furthermore, a concrete numerical example is provided using the Picard iteration method to demonstrate the feasibility, accuracy and effectiveness of the proposed theoretical framework. This validates the applicability of the approach to a class of memory-dependent dynamical systems with complex delay structures.