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<p>Fractional differential equations excel at modeling memory and hereditary effects, offering distinct advantages over integer-order models in describing complex dynamic behaviors. This paper investigates the solutions for nonlinear fractional coupled systems with Caputo derivative-dependent impulses and mixed integral-differential boundary conditions. Unlike existing literature, we introduce nonlinear impulses coupled with fractional derivatives and coupled nonlocal integral boundary conditions, which better reflect real-world scenarios such as pulsed drug release, neural networks, and viscoelastic control systems. By constructing a weighted normed space and deriving refined Green’s function estimates, we establish sufficient conditions for the existence and uniqueness of solutions using Banach’s contraction mapping principle and Krasnoselskii’s fixed point theorem. A numerical example is provided to validate the theoretical results and further analyze the influence of impulse strength and fractional orders on system dynamics. The findings extend the theoretical framework of fractional impulsive coupled systems and provide new methodologies for modeling complex dynamic processes.</p>

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Research on fractional-order nonlinear coupled systems subject to impulsive mixed boundary value problems

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月27日

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  • Weide Liu,
  • Huixing Zhu,
  • Chunmiao Huang

摘要

Fractional differential equations excel at modeling memory and hereditary effects, offering distinct advantages over integer-order models in describing complex dynamic behaviors. This paper investigates the solutions for nonlinear fractional coupled systems with Caputo derivative-dependent impulses and mixed integral-differential boundary conditions. Unlike existing literature, we introduce nonlinear impulses coupled with fractional derivatives and coupled nonlocal integral boundary conditions, which better reflect real-world scenarios such as pulsed drug release, neural networks, and viscoelastic control systems. By constructing a weighted normed space and deriving refined Green’s function estimates, we establish sufficient conditions for the existence and uniqueness of solutions using Banach’s contraction mapping principle and Krasnoselskii’s fixed point theorem. A numerical example is provided to validate the theoretical results and further analyze the influence of impulse strength and fractional orders on system dynamics. The findings extend the theoretical framework of fractional impulsive coupled systems and provide new methodologies for modeling complex dynamic processes.