Research on fractional-order nonlinear coupled systems subject to impulsive mixed boundary value problems
- 1School of Mathematical Sciences & Center for Applied Mathematics of Guangxi, Guangxi Minzu University
- 2School of Information Engineering, Zhengzhou Shengda Institute of Economics and Management
- 3College of Education, Guangxi Vocational Normal University
Abstract
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.
Related
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BibTeX
@article{liu2026research,
title = {{Research on fractional-order nonlinear coupled systems subject to impulsive mixed boundary value problems}},
author = {Weide Liu and Huixing Zhu and Chunmiao Huang},
journal = {Journal of Inequalities and Applications},
year = {2026},
month = jul,
doi = {10.1186/s13660-026-03518-4},
url = {https://doi.org/10.1186/s13660-026-03518-4},
note = {CC BY},
}
RIS
TY - JOUR
TI - Research on fractional-order nonlinear coupled systems subject to impulsive mixed boundary value problems
AU - Weide Liu
AU - Huixing Zhu
AU - Chunmiao Huang
PY - 2026
DA - 2026/07/01
JO - Journal of Inequalities and Applications
DO - 10.1186/s13660-026-03518-4
UR - https://doi.org/10.1186/s13660-026-03518-4
AB - 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.
SN - 1029-242X
ER -