A general fractional breast cancer model: Model graph energy, Caputo-Fabrizio derivative existence and uniqueness plus numerical simulation

Abstract

In the study of epidemiology, mathematical modelling is crucial because it improves understanding of the underlying mechanisms that cause illnesses to spread and offers the possibility of developing preventative interventions. In this paper, we have discussed a fractional mathematical model. A set of fractional differential equations is used to build the model. We have applied a Caputo Fabrizio (CF) to describe the fractional breast cancer model. The model consists of five subpopulations that make up a population. They are disease-free (D), cardiotoxic (E), stages 1 and 2 (A), 3 (B), and 4 (C). We have used a digraph chart to present the breast cancer model. We have used some graph theory concepts to compute the energy of the breast cancer model corresponding digraph. We have demonstrated the existence, uniqueness, and positivity of the model solutions. The fixed point hypothesis demonstrates both the existence of a solution to the suggested fractional breast cancer model as well as the fact that this solution is one of a kind. Numerical simulations are a useful tool for explaining the suggested notion. We have presented a numerical method for simulating the problem. We have used an algorithm modelled after the Adams-Bashforth-Moulton method (ABMM) to solve the model. Numerical simulations of the model in various fractional orders illustrate the theoretical conclusions. We have used the Matlab application to calculate every solution. The results demonstrate the efficacy of the proposed fractional model from an epidemiological standpoint.