The numerical analysis of Caputo-Fabrizio fractional mathematical model of Cancer Chemotherapy

Abstract

In this study, the numerical solutions of the Caputo-Fabrizio fractional mathematical model of cancer chemotherapy are investigated using the Caputo-Fabrizio q-Elzaki homotopy analysis transform technique (CFqEHATT) and the Caputo-Fabrizio Elzaki Adomian decomposition method (CFEADM). Cancer is a neoplastic disease characterized by uncontrolled cell proliferation. The objective of this work is to develop an accurate and efficient numerical framework for analyzing the dynamics of tumor cells, immune cells, normal cells, and chemotherapeutic drugs under the influence of memory effects inherent in biological systems. The CaputoFabrizio fractional operator, which employs an exponential kernel without singularity, is particularly suitable for modeling such memory-dependent processes in cancer progression and treatment response. The proposed methods are applied to a system modeling the interactions among tumor cells, immune cells, normal cells, and chemotherapeutic drugs. The numerical solutions are illustrated through 2D and 3D graphical representations, and comparative simulations are presented in tabular form, demonstrating the efficiency and consistency of the CFq-EHATT and CFEADM. The results highlight the influence of the fractional order on the system dynamics, offering deeper insights into chemotherapy optimization and tumor evolution, thus contributing to the advancement of mathematical oncology. Mathematics Subject Classification: 35R11 - 35C05 - 65R10.