Approximate analytical solutions and application to logistic models with fractional derivatives

A powerful tool to investigate hypotheses, verify experimental results and simulate the dynamics of complex systems is mathematical modeling. Different versions and generalizations of the logistic growth model have been considered. The nonlinear nature of the most mathematical models has called for the introduction of diverse techniques to obtain their solutions. This paper introduces a generalized form of the logistic growth model, which incorporates and improves some existing models as special cases. Moreover, the paper presents an approximate analytical method that is potent in treating the nonlinear fractional differential equations with time delay and applies it to the logistic models. Lastly, the paper presents some numerical experiments and displays the dynamics of logistic models with Caputo-fractional derivative and time delay to show that the approximate analytical method always yields reliable solutions.