使用修改的He-Laplace算法对时间分数癌症瘤模型的新解决方案
Mubashir Qayyum1, Efaza Ahmad1, Mohamed R Ali2,3
1Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore, Pakistan.
Heliyon
|December 13, 2024
概括
这项研究引入了一种具有新杀伤率的概括分数癌症瘤模型. 拟议的混合方法有效地分析分数导数,显示最小的误差和复杂瘤动态的可靠结果.
科学领域:
- 数学瘤学数学瘤学
- 计算生物学 计算生物学
- 分数微积分的计算.
背景情况:
- 癌症的扩散源于控制细胞生长的基因突变.
- 现有的癌症模型正在用微积分计算来增强,以提高准确性.
- 了解瘤动态需要复杂的数学建模.
研究的目的:
- 在微积分计算框架内研究一个通用的癌症瘤模型.
- 为了结合时间依赖,位置依赖和度依赖的杀戮率.
- 开发一种高效的计算算法,用于分析分数瘤模型.
主要方法:
- 一种混合计算方法,结合了同位点扰动和拉普拉斯变换.
- 使用数学定理对收和误差极限进行理论分析.
- 在整个分数域中对算法的精度和性能进行数值验证.
主要成果:
- 拟议的混合算法有效地处理各种分数导数.
- 理论和数值分析证实,在分数域内计算的误差很低.
- 图形比较揭示了不同类型的分数导数 (Caputo,CF,AB) 对瘤模型解决方案的影响.
结论:
- 开发的方法对于复杂的分数瘤模型是可靠的.
- 该方法证明了其对其他复杂物理现象的潜在适用性.
- 这项工作推进了癌症生长动态的数学建模.
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