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Abstract：
Cancer, a complex and deadly health concern today, is characterized by forming potentially malignant tumors or cancer cells. The dynamic interaction between these cells and their environment is crucial to the disease. Mathematical models can enhance our understanding of these interactions, helping us predict disease progression and treatment strategies.
In this study, we develop a fractional tumor-immune interaction model specifically for lung cancer (FTIIM-LC). We present some definitions and significant results related to the Caputo operator. We employ the generalized Laguerre polynomials (GLPs) method to find the optimal solution for the FTIIM-LC model. We then conduct a numerical simulation and compare the results of our method with other techniques and real-world data.
We propose a FTIIM-LC model in this paper. The approximate solution for the proposed model is derived using a series of expansions in a new set of polynomials, the GLPs. To streamline the process, we integrate Lagrange multipliers, GLPs, and operational matrices of fractional and ordinary derivatives. We conduct a numerical simulation to study the effects of varying fractional orders and achieve the expected theoretical results.
The findings of this study demonstrate that the optimization methods used can effectively predict and analyze complex phenomena. This innovative approach can also be applied to other nonlinear differential equations, such as the fractional Klein-Gordon equation, fractional diffusion-wave equation, breast cancer model, and fractional optimal control problems.
In this study, we develop a fractional tumor-immune interaction model specifically for lung cancer (FTIIM-LC). We present some definitions and significant results related to the Caputo operator. We employ the generalized Laguerre polynomials (GLPs) method to find the optimal solution for the FTIIM-LC model. We then conduct a numerical simulation and compare the results of our method with other techniques and real-world data.
We propose a FTIIM-LC model in this paper. The approximate solution for the proposed model is derived using a series of expansions in a new set of polynomials, the GLPs. To streamline the process, we integrate Lagrange multipliers, GLPs, and operational matrices of fractional and ordinary derivatives. We conduct a numerical simulation to study the effects of varying fractional orders and achieve the expected theoretical results.
The findings of this study demonstrate that the optimization methods used can effectively predict and analyze complex phenomena. This innovative approach can also be applied to other nonlinear differential equations, such as the fractional Klein-Gordon equation, fractional diffusion-wave equation, breast cancer model, and fractional optimal control problems.
摘要：
背景：癌症，今天是一个复杂而致命的健康问题，其特征在于形成潜在的恶性肿瘤或癌细胞。这些细胞与其环境之间的动态相互作用对疾病至关重要。数学模型可以增强我们对这些相互作用的理解，帮助我们预测疾病进展和治疗策略。
方法：在本研究中，我们建立了专门针对肺癌的部分肿瘤-免疫相互作用模型(FTIM-LC).我们提供了一些与Caputo运算符相关的定义和重要结果。我们采用广义拉盖尔多项式（GLPs）方法来找到FTIM-LC模型的最佳解决方案。然后，我们进行了数值模拟，并将我们方法的结果与其他技术和实际数据进行了比较。
结果：我们在本文中提出了FTIM-LC模型。所提出的模型的近似解是使用一组新多项式中的一系列展开得出的，GLPs。为了简化流程，我们集成了拉格朗日乘数，GLPs,以及分数阶和普通阶导数的运算矩阵。我们进行了数值模拟，研究了不同分数阶的影响，并获得了预期的理论结果。
结论：这项研究的结果表明，所使用的优化方法可以有效地预测和分析复杂现象。这种创新的方法也可以应用于其他非线性微分方程，比如分数阶Klein-Gordon方程,分数阶扩散波方程，乳腺癌模型，和分数阶最优控制问题。
方法：在本研究中，我们建立了专门针对肺癌的部分肿瘤-免疫相互作用模型(FTIM-LC).我们提供了一些与Caputo运算符相关的定义和重要结果。我们采用广义拉盖尔多项式（GLPs）方法来找到FTIM-LC模型的最佳解决方案。然后，我们进行了数值模拟，并将我们方法的结果与其他技术和实际数据进行了比较。
结果：我们在本文中提出了FTIM-LC模型。所提出的模型的近似解是使用一组新多项式中的一系列展开得出的，GLPs。为了简化流程，我们集成了拉格朗日乘数，GLPs,以及分数阶和普通阶导数的运算矩阵。我们进行了数值模拟，研究了不同分数阶的影响，并获得了预期的理论结果。
结论：这项研究的结果表明，所使用的优化方法可以有效地预测和分析复杂现象。这种创新的方法也可以应用于其他非线性微分方程，比如分数阶Klein-Gordon方程,分数阶扩散波方程，乳腺癌模型，和分数阶最优控制问题。
