Analyzing the impact of time-fractional models on chemotherapy's effect on cancer cells

In this study, we employ the Laplace Variational Iterational Method (LVIM) as a sophisticated mathematical tool to investigate into the complex dynamics of cancer cells under the influence of chemotherapy. The LVIM, a method combining Laplace transformations and variational iteration techniques, is specifically adapted to address a system of time fractional differential equations (FDEs) that characterizes the temporal behavior of cancer cells. To enhance the efficacy of our approach, we introduce a semi-analytic version of LVIM, which proves to be a powerful and versatile tool for solving mathematical problems involving fractional derivatives. The focus of our analysis centers on elucidating the impact of chemotherapy, with a particular emphasis on drug diffusion within cancer cells and the fractality of DNA walks. Through numerical exploration encompassing varying fractional order derivatives, our study exposes nonlinear behaviors that remain secret in systems featuring only integer order derivatives. Notably, the methodology we propose is not only applicable to the specific cases examined in this research but also exhibits broad versatility, making it suitable for exploring the effects of different drugs and types of cancers. This research contributes valuable insights into the dynamics of cancer cells, aiding in the understanding of the implications for therapeutic strategies in the context of cancer treatment.