Dynamical analysis of a Tumor-Macrophages interaction model governed by the Caputo-Fabrizio derivatives

The Caputo-Fabrizio derivative is considered to be one of the most successful tools of fractional modeling since it has non singular nuclei, which make it a better candidate for modeling some interdisciplinary models that rely on memory effects and hereditary features such as the mathematical models in biology. In this study, tumor-macrophages interactions are modeled via the Caputo-Fabrizio derivatives. The uniqueness of the model's solutions is shown. A convergence analysis based on the Adomian decomposition method (ADM) is proved. The error analysis using the ADM is discussed. The Picard method is applied to the considered model. According to the stability theory of fractional-order systems governed by the Caputo-Fabrizio derivatives, the stability conditions of the tumor-free, the tumor-dominant, and the co-axial or the existence equilibrium points are discussed. Numerical simulations are carried out to show the rich complex dynamics in the model, including the existence of chaotic attractors.