Numerical Analysis of Time-Fractional Cancer Models with Different Types of Net Killing Rate

Hami Gündoǧdu and Hardik Joshi ()
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Hami Gündoǧdu: Department of Mathematics, Faculty of Science, Sakarya University, Serdivan 54050, Turkey
Hardik Joshi: Department of Mathematics, LJ Institute of Engineering and Technology, LJ University, Ahmedabad 382210, Gujarat, India

Mathematics, 2025, vol. 13, issue 3, 1-18

Abstract: This study introduces a novel approach to modeling cancer tumor dynamics within a fractional framework, emphasizing the critical role of the net killing rate in determining tumor growth or decay. We explore a generalized cancer model where the net killing rate is considered across three domains: time-dependent, position-dependent, and concentration-dependent. The primary objective is to derive an analytical solution for time-fractional cancer models using the Residual Power Series Method (RPSM), a technique not previously applied in this conformable context. Traditional methods for solving fractional-order differential models face challenges such as perturbations, complex simplifications, discretization issues, and restrictive assumptions. In contrast, the RPSM overcomes these limitations by offering a robust solution that reduces both complexity and computational effort. The method provides exact analytical solutions through a convergence series and reliable numerical approximations when needed, making it a versatile tool for simulating fractional-order cancer models. Graphical representations of the approximate solutions illustrate the method’s effectiveness and applicability. The findings highlight the RPSM’s potential to advance cancer treatment strategies by providing a more precise understanding of tumor dynamics in a fractional context. This work contributes to both theoretical and practical advancements in cancer research and lays the groundwork for more accurate and efficient modeling of cancer dynamics, ultimately aiding in the development of optimal treatment strategies.

Keywords: time-fractional cancer models; net killing rate; concentration of cancer over time; residual power series method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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