Fractional Order Solution to Analyze Tumor-Immune Cells by Using Hybrid Natural Transform Method and Residual Power Series Method (Journal of Nonlinear Modeling and Analysis, 2025)
The purpose of this study is to examine the impact of fractional-order chemotherapy drug diffusion on tumor-immune cell growth. To address the proposed system of fractional-order tumor-immune cell dynamics, two distinct and robust methods have been employed. Initially, the Hybrid Natural Decomposition method, an analytical approach that merges two effective techniques – Natural Transform and the Adomian Decomposition Method has been applied. Subsequently, the Residual Power Series method, a numerical technique, has been employed to derive the solution in series form. The graphical comparison of the results obtained from both methods with those from classical-order solutions has been provided. The findings clearly demonstrate that the proposed approaches offer a reliable and accurate means of understanding the intricate interactions between tumor growth and immune cell activity.
Keywords: Chemotherapy; cancer; Residual Power Series method; Natural Transform method; tumor immune cell; fractional derivative; Adomian polynomials