Numerical and analytical study of fractional order tumor model through modeling with treatment of chemotherapy

Cancer is the world’s second-biggest cause of death, accounting for roughly 10 million deaths in 2020 and estimated to reach 16 million by 2040. In this study, we propose a novel technique for the treatment of tumor models with a power-law kernel with the Sumudu transform. The analysis was made for a generalized form of analytical solution that is unique and Picard K-stable by using Hilbert and Banach space results. The model investigates the Ulam-Hyers-Rassias stability, uniqueness of solutions, and impact of fractional derivatives with the power-law kernel. Reproductive number analysis with an equilibrium point shows the bounded solution in the feasible region. In the end, numerical simulations are drawn through figures at different fractional and fractal dimensions for the dynamics of treatment and the growth of normal cells. The analysis shows crucial criteria for system stability, ensuring the efficacy of therapeutic interventions through novel mathematical and biological insights.