This paper presents an analytical and numerical investigation of cancer tumor dynamics modeled by a fractional partial differential equation, incorporating the cancer cell killing ratio to represent the efficacy of treatment over time. The fractional partial differential equation framework offers a more flexible model of tumor growth dynamics than traditional integer-order models, capturing the memory and hereditary properties often observed in cancer progression. The Homotopy Analysis Method, a semi-analytical approach, is employed to obtain an approximate series of solutions to the model, allowing for an adjustable convergence of results. In addition, the Chebyshev Collocation Method is applied as a numerical solution technique, providing high accuracy with fewer computational nodes, and efficiently capturing the intricate dynamics of tumor growth. The study compares solutions from both methods, highlighting the impact of fractional order and treatment parameters on tumor reduction rates. Graphical representations demonstrate the effect of the variable killing percentage on tumor dynamics, underscoring the potential of FPDEs in enhancing the predictive accuracy of cancer treatment models.
Shahin et al. (Wed,) studied this question.