Scholarlink

<p>A lot of fractal-fractional mathematical models lack time dimensionality balance. This raises questions on its approach toward physical meaning to real-world problems. Our study investigates the underlying issue by considering a simple yet new colorectal cancer model incorporating cetuximab administration with the effect of memory, and considering average human body’s measurement. An analytical solution of the system is found using the Sumudu transform. Also, using Hilbert and Banach space theories, an analysis was performed for a generalized form of unique and Picard <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2464_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal{H}\)</EquationSource> </InlineEquation>-stable analytical solution. The proposed model explores the uniqueness of solutions, transcritical bifurcation, and Ulam-Hyers stability. Some new biological insights in terms of fractional parameters are suggested. Finally, numerical simulations for the dynamics of medical therapy in eradicating malignancy are depicted for various fractional and fractal dimensions. The necessity of the cetuximab drug is also highlighted together with the proliferation of the effector cells. The analysis provides new bio-mathematical understandings that guarantee the effectiveness of therapeutic interventions by illuminating critical criteria for system stability. One of the major significances of the proposed model is predicting the consistency of the treatment by carrying the numerical simulations for the model.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Mathematical analysis of a new dimensionalized fractal-fractional operator with application to colorectal cancer treatment model

  • 期刊论文

  • 发表日期：

    2025年4月18日

查看全文
  • Biplab Dhar,
  • Manisha Malik

摘要

A lot of fractal-fractional mathematical models lack time dimensionality balance. This raises questions on its approach toward physical meaning to real-world problems. Our study investigates the underlying issue by considering a simple yet new colorectal cancer model incorporating cetuximab administration with the effect of memory, and considering average human body’s measurement. An analytical solution of the system is found using the Sumudu transform. Also, using Hilbert and Banach space theories, an analysis was performed for a generalized form of unique and Picard \(\mathcal{H}\) -stable analytical solution. The proposed model explores the uniqueness of solutions, transcritical bifurcation, and Ulam-Hyers stability. Some new biological insights in terms of fractional parameters are suggested. Finally, numerical simulations for the dynamics of medical therapy in eradicating malignancy are depicted for various fractional and fractal dimensions. The necessity of the cetuximab drug is also highlighted together with the proliferation of the effector cells. The analysis provides new bio-mathematical understandings that guarantee the effectiveness of therapeutic interventions by illuminating critical criteria for system stability. One of the major significances of the proposed model is predicting the consistency of the treatment by carrying the numerical simulations for the model.