Investigating Pancreatic Cancer Dynamics Through Fractional Modeling With Caputo Derivative

IF 1.8 3区 数学 Q1 MATHEMATICS, APPLIED
Mihir Thakkar, Anil Chavada, Nimisha Pathak
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引用次数: 0

Abstract

This research investigates the interplay among pancreatic cancer cells (PCCs), pancreatic stellate cells (PSC), effector cells, and both tumor-suppressing and tumor-promoting cytokines to better understand the dynamics of pancreatic cancer. Using the Caputo fractional derivative, the traditional model is transformed into a fractional-order framework while maintaining dimensional consistency in its equations. The study examines equilibrium points, with a specific focus on the tumor-free and high-tumor state, to evaluate local stability. The fixed-point theorem is applied to confirm the existence and uniqueness of solutions, and global stability is established through the Hyers–Ulam–Rassias method. Numerical simulations, carried out using the zwo-step Adams-Bashforth method across various fractional orders, unveil the system's complex behaviors. These results contribute to a deeper understanding of pancreatic cancer dynamics and provide meaningful insights into its underlying mechanisms.

Abstract Image

用Caputo导数的分数模型研究胰腺癌动力学
本研究旨在探讨胰腺癌细胞(PCCs)、胰腺星状细胞(PSC)、效应细胞以及肿瘤抑制因子和肿瘤促进因子之间的相互作用,以更好地了解胰腺癌的动态。利用Caputo分数阶导数,将传统模型转化为分数阶框架,同时保持方程的维数一致性。该研究检查平衡点,特别关注无肿瘤和高肿瘤状态,以评估局部稳定性。利用不动点定理证实了解的存在唯一性,并利用Hyers-Ulam-Rassias方法建立了全局稳定性。采用不同分数阶的双步Adams-Bashforth方法进行的数值模拟揭示了系统的复杂行为。这些结果有助于更深入地了解胰腺癌动力学,并为其潜在机制提供有意义的见解。
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来源期刊
CiteScore
4.90
自引率
6.90%
发文量
798
审稿时长
6 months
期刊介绍: Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.
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