通过不变点技术使用卡普托分数顺序导数的块性皮肤病的数学模型
Gunaseelan Mani1, Arul Joseph Gnanaprakasam2, Sakthi Ramalingam3
1Department of Mathematics, Saveetha Institute of Medical and Technical Sciences, Saveetha School of Engineering, Saveetha University, Chennai, Tamil Nadu, 602105, India.
Scientific reports
|March 18, 2025
概括
这项研究应用了使用卡普托-法布里齐奥分数导数的分数模型来分析块性皮肤疾病的动态. 分数分析显示,与传统方法相比,模拟疾病进展的准确性提高了.
科学领域:
- 流行病学 流行病学
- 数学生物学 数学生物学
- 分数微积分的计算.
背景情况:
- 凸起性皮肤病 (LSD) 对全球牛群构成重大威胁.
- 现有的数学模型经常使用整数顺序导数,这可能会限制它们捕捉复杂疾病动态的能力.
研究的目的:
- 通过使用卡普托-法布里齐奥分数 (CFF) 衍生来研究块性皮肤病 (LSD) 的分数模型.
- 分析LSD模型的解决方案的存在和独特性.
- 探索分数顺序对疾病动态和控制参数的影响.
主要方法:
- 在LSD模型中应用卡普托-法布里齐奥分数导数.
- 使用Picard-Lindelof方法进行存在和独特性分析.
- 采用数字技术,包括分数微积分的基本定理和固定点定理,以获得接近形式的解决方案.
- 进行数值模拟,以评估控制参数和分数顺序的影响.
主要成果:
- 确定了分数LSD模型的解决方案的存在和独特性.
- 数值模拟表明,与整数顺序模型相比,分数顺序导数提供了更准确的LSD动态表示.
- 该研究强调了控制参数对疾病在不同分数顺序的不同模型组中传播的显著影响.
结论:
- 分数分析,特别是使用CFF衍生品,在建模块性皮肤疾病中提供了更高的准确性.
- 这些发现有助于更深入地了解LSD动态,并可能为改进的疾病控制和管理策略提供信息.
- 分数模型的几何表示为其复杂性和可靠性提供了洞察力.
相关概念视频
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