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<p>This paper examines the role of time delays in epidemic models, taking advantage of fractional delay differential equations. By adopting an innovative combination of large shrinkage mappings and Chatterjea-type mappings, the paper builds upon established theoretical foundations to develop a novel analytical and numerical framework for investigating the influence of time delays in fractional epidemic models. With the aim of linking these findings to real-world applications, a numerical simulation framework is presented to study the dynamics of a generalized fractional-delay epidemic system, incorporating time-dependent effects that influence disease transmission and stability. By incorporating Caputo’s fractional derivative, the results reveal the impact of time delays, such as incubation periods, and fractional dynamics on disease transmission and stability in the system. These results shed light on the complex interactions between time delays and the fractal properties of the system, providing a comprehensive approach to modeling evolving temporal behaviors in epidemiology.</p>

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Theoretical analysis and applications of fixed-point theorems in delay fractional differential equations

  • 期刊论文

  • 发表日期：

    2025年5月7日

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  • Mohamed Balegh,
  • Ahmed GhezaL

摘要

This paper examines the role of time delays in epidemic models, taking advantage of fractional delay differential equations. By adopting an innovative combination of large shrinkage mappings and Chatterjea-type mappings, the paper builds upon established theoretical foundations to develop a novel analytical and numerical framework for investigating the influence of time delays in fractional epidemic models. With the aim of linking these findings to real-world applications, a numerical simulation framework is presented to study the dynamics of a generalized fractional-delay epidemic system, incorporating time-dependent effects that influence disease transmission and stability. By incorporating Caputo’s fractional derivative, the results reveal the impact of time delays, such as incubation periods, and fractional dynamics on disease transmission and stability in the system. These results shed light on the complex interactions between time delays and the fractal properties of the system, providing a comprehensive approach to modeling evolving temporal behaviors in epidemiology.