将广义玛函数应用于分数级生物系统的应用
A E Matouk1,2
1Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah, 11952, Saudi Arabia.
Heliyon
|August 16, 2023
概括
本研究引入了新的分数运算符,以探索抗菌素耐药性 (AMR) 模型中的复杂动态. 这些操作者揭示了分叉,吸引力和混乱,为AMR系统行为提供了新的见解.
科学领域:
- 数学建模的数学建模
- 动态系统理论 动态系统理论
- 流行病学 流行病学
背景情况:
- 抗菌素耐药性 (AMR) 构成了全球健康的重大威胁.
- 分数阶微分方程为模拟像AMR这样的复杂生物现象提供了强大的框架.
- 现有的模型可能无法完全捕捉AMR传播中固有的复杂动态.
研究的目的:
- 引入和分析新的扩展左和右卡普托分数微分运算符 (ELCFDO和ERCFDO).
- 调查由包含这些新运营商的分数级AMR模型产生的复杂动态.
- 扩展分数-分数运算符 (FFO) 并将其应用于AMR模型进行进一步分析.
主要方法:
- 介绍ELCFDO和ERCFDO及其属性的分析.
- 使用零碎常数参数对分数AMR模型进行分离.
- 对二叉曲线 (尼马克-萨克,翻转),封闭不变曲线和混乱/碎形吸引器的研究.
- 将FFO扩展到EFFO,并将其应用于AMR系统.
主要成果:
- 在ELCFDO引入了一个新的微分参数,影响AMR模型中的复杂动态.
- 离散模型展示了尼马克-萨克和翻转的分叉,封闭的不变曲线和奇怪/混乱的吸引力.
- 扩展分数-分数运算符 (EFFO) 也在抗药性系统中产生复杂的动态,与分数运算符一致.
结论:
- 开发的分数运算符及其离散形式有效地揭示了AMR模型中复杂的动态行为.
- 该研究强调了分数计算和分数-分数计算在了解AMR方面的潜力.
- 这些发现有助于更深入地了解AMR系统动态,并可以为控制策略提供信息.
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