基于Ψ-Caputo导数和Mittag-Leffler定律的乳腺癌交叉数学模型比较研究:数值处理

Symmetry Pub Date : 2024-09-06 DOI:10.3390/sym16091172
Nasser H. Sweilam, Seham M. Al-Mekhlafi, Waleed S. Abdel Kareem, Ghader Alqurishi
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引用次数: 0

摘要

两种新型乳腺癌交叉模型包含Ψ-卡普托分形变阶分形导数、分形分阶导数和变阶分形布朗运动驱动的变阶分形随机导数,以及包含Atangana-Baleanu Caputo分形变阶分形导数的乳腺癌交叉模型、我们在第一个模型中使用了简单的非标准核函数Ψ(t),在第二个模型中使用了非矢量核函数Ψ(t)。此外,我们还利用沙特阿拉伯的实际统计数据对我们的模型进行了评估。为了确保与物理模型问题的一致性,我们引入了对称参数 ζ。我们可以从提出的Ψ-卡普托导数得到分形变阶分数卡普托和卡普托-卡图甘波拉导数作为特例。交叉动力学模型定义了三种可选模型:分形变阶分数模型、分形分数阶模型和三时间间隔变阶分数随机模型。分析了拟议模型的稳定性。设计了Ψ-非标准有限差分法来求解分形变阶分形模型和分形分形模型,并使用 Toufik-Atangana 法求解非矢量核的第二次交叉模型。此外,还使用了非标准修正欧拉-马鲁山方法来研究变阶分数随机模型。为了验证这些方法的有效性并支持理论结论,我们进行了大量的数值测试并与实际数据进行了比较。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Comparative Study of Crossover Mathematical Model of Breast Cancer Based on Ψ-Caputo Derivative and Mittag-Leffler Laws: Numerical Treatments
Two novel crossover models for breast cancer that incorporate Ψ-Caputo fractal variable-order fractional derivatives, fractal fractional-order derivatives, and variable-order fractional stochastic derivatives driven by variable-order fractional Brownian motion and the crossover model for breast cancer that incorporates Atangana–Baleanu Caputo fractal variable-order fractional derivatives, fractal fractional-order derivatives, and variable-order fractional stochastic derivatives driven by variable-order fractional Brownian motion are presented here, where we used a simple nonstandard kernel function Ψ(t) in the first model and a non-singular kernel in the second model. Moreover, we evaluated our models using actual statistics from Saudi Arabia. To ensure consistency with the physical model problem, the symmetry parameter ζ is introduced. We can obtain the fractal variable-order fractional Caputo and Caputo–Katugampola derivatives as special cases from the proposed Ψ-Caputo derivative. The crossover dynamics models define three alternative models: fractal variable-order fractional model, fractal fractional-order model, and variable-order fractional stochastic model over three-time intervals. The stability of the proposed model is analyzed. The Ψ-nonstandard finite-difference method is designed to solve fractal variable-order fractional and fractal fractional models, and the Toufik–Atangana method is used to solve the second crossover model with the non-singular kernel. Also, the nonstandard modified Euler–Maruyama method is used to study the variable-order fractional stochastic model. Numerous numerical tests and comparisons with real data were conducted to validate the methods’ efficacy and support the theoretical conclusions.
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