Exploration of time-fractional cancer tumor models with variable cell killing rates via hybrid algorithm

Abstract

Cancer is marked by abnormal cell growth that invades healthy tissues, potentially spreading throughout the body through the bloodstream or lymphatic system. It arises when body cells show irregularities in the genes that control cell growth. To treat and minimize the growth of these abnormal cells, different models have been proposed to predict and analyze cancer-tumor. The current study contains analysis of fractional cancer-tumor with different uncertain conditions. To include the uncertainties in the model, Pentagonal fuzzy numbers (PFNs) approach is utilized. A hybrid mechanism, combining homotopies with perturbation technique and a generalized integral transform, is proposed to efficiently handle fractional derivatives with fuzzified conditions. The validity of obtained solutions is checked by calculating residual errors. Graphical analysis assesses the impact of important parameters on the solution profiles, and confirms the reliability of the proposed methodology for complex fractional tumor models and other intricate physical phenomena.