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Optimizing fractional mathematical frameworks for cancer tumor analysis with residual power series

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  • Alharbi, Weam G.
  • Maneea, M.
  • Ali, Khalid K.

Abstract

In this paper, we employ the Residual Power Series Method (RPSM) to derive an approximate computational solution for a mathematical model of cancer tumors. Our study specifically examines the effects of chemotherapy on cancer, investigating the interactions among chemotherapeutic agents, tumor cells, normal cells, and immune cells within the framework of fractional partial differential equations (FPDEs). The RPSM is utilized to deliver highly accurate solutions in the form of series with rapid convergence, even for nonlinear and complex models. Mathematical modeling is essential for exploring hypotheses related to biological phenomena, particularly in recent decades, where significant advancements have been made in predicting chemotherapy outcomes through the modeling of tumor-immune system interactions. In this research, we analyze the impact of cancer tumors through a system of FPDEs defined by the Caputo derivative. We present two- and three-dimensional graphs to illustrate the relationships between various parameters and variables, thereby demonstrating the effects of chemotherapy on cellular dynamics.

Suggested Citation

  • Alharbi, Weam G. & Maneea, M. & Ali, Khalid K., 2025. "Optimizing fractional mathematical frameworks for cancer tumor analysis with residual power series," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:chsofr:v:194:y:2025:i:c:s0960077925001705
    DOI: 10.1016/j.chaos.2025.116157
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    References listed on IDEAS

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    1. A. Elsaid & M. S. Abdel Latif & M. Maneea, 2016. "Similarity Solutions for Multiterm Time‐Fractional Diffusion Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2016(1).
    2. Kumar, Sunil & Kumar, Ajay & Samet, Bessem & Gómez-Aguilar, J.F. & Osman, M.S., 2020. "A chaos study of tumor and effector cells in fractional tumor-immune model for cancer treatment," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    3. A. Elsaid & M. S. Abdel Latif & M. Maneea, 2016. "Similarity Solutions for Multiterm Time-Fractional Diffusion Equation," Advances in Mathematical Physics, Hindawi, vol. 2016, pages 1-7, May.
    4. Ali, Khalid K. & Wazwaz, Abdul-Majid & Maneea, M., 2024. "Efficient solutions for fractional Tsunami shallow-water mathematical model: A comparative study via semi analytical techniques," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    5. Aliaa Burqan & Mona Khandaqji & Zeyad Al-Zhour & Ahmad El-Ajou & Tasneem Alrahamneh & Fernando Simoes, 2024. "Analytical Approximate Solutions of Caputo Fractional KdV-Burgers Equations Using Laplace Residual Power Series Technique," Journal of Applied Mathematics, Hindawi, vol. 2024, pages 1-19, March.
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