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<p>Tomatoes rank as the second most important vegetable crop globally, making their health and productivity a critical concern. Tomato Yellow Leaf Curl (TYLC) disease poses a significant threat, necessitating focused research due to its widespread impact on this highly consumed vegetable. This study presents an empirical analysis to better understand and address the disease’s effects. It explores a system of fractional differential equations, employing the Caputo-Fabrizio (C-F) fractional operator, to model the interaction between tomato plants and viruses within a crop field. The model focuses on exploring optimal control strategies aimed at mitigating the spread of the Tomato Yellow Leaf Curl (TYLC) disease. The optimal control problem is rigorously analyzed using Pontryagin’s Maximum Principle (PMP), leading to the derivation of an optimality system. The resulting system is numerically simulated through a forward-backward sweep algorithm. These simulations effectively demonstrate the impact of various control intervention combinations on the disease’s transmission dynamics.</p>

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A Caputo-Fabrizio fractional optimal control framework, analysis and simulation for the dynamics of tomato yellow leaf curl disease

  • 期刊论文

  • 发表日期：

    2026年7月12日

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  • Ritu Agarwal,
  • Chhaya Midha

摘要

Tomatoes rank as the second most important vegetable crop globally, making their health and productivity a critical concern. Tomato Yellow Leaf Curl (TYLC) disease poses a significant threat, necessitating focused research due to its widespread impact on this highly consumed vegetable. This study presents an empirical analysis to better understand and address the disease’s effects. It explores a system of fractional differential equations, employing the Caputo-Fabrizio (C-F) fractional operator, to model the interaction between tomato plants and viruses within a crop field. The model focuses on exploring optimal control strategies aimed at mitigating the spread of the Tomato Yellow Leaf Curl (TYLC) disease. The optimal control problem is rigorously analyzed using Pontryagin’s Maximum Principle (PMP), leading to the derivation of an optimality system. The resulting system is numerically simulated through a forward-backward sweep algorithm. These simulations effectively demonstrate the impact of various control intervention combinations on the disease’s transmission dynamics.