Crossover behaviors via piecewise concept: A model of tumor growth and its response to radiotherapy

This study aims to combine 3 different models, which take into account the pre-treatment, during the treatment and post-treatment processes of the tumor growth, with the piecewise derivative, and to consider these processes as a whole thanks to this new concept. This concept leads us to analyze and predict the process from the beginning to the end of the tumor, as it offers the possibility to observe many behaviors from crossover to stochastic processes. Moreover, the piecewise differential operators, which can be constructed with operators such as classical, Caputo, Caputo-Fabrizio, Atangana-Baleanu and stochastic derivative, have opened new doors to readers in different disciplines and enable them to capture different behaviors in different time intervals. Thus, researchers can achieve successful results in capturing reality by applying these operators to real-world problems.