Analytical solutions, limiting sizes, and blow-up times of several well-known fractional nonlinear tumor growth models

This paper applies Laplace transform and Mittag-Leffler function to obtain analytical solutions of some fractional tumor growth models, including Exponential, Logistic, Gompertz and Bertalanffy–Pütter models. We present the tumor growth curves of these four models for comparison under different fractional and integer orders. It shows that compared to first-order differential equation models, their corresponding fractional differential equation models can provide more choices based on the change of fractional order ([Formula: see text]) to better characterize the evolution of models and more accurately predict the blow-up times of certain tumors.