Abstract
In this study, we examine and analyze the solution for the pediculosis disease model utilizing the predictor-corrector approach in relation to the Caputo fractional derivative. The existence and uniqueness of the selected model have been examined. Furthermore, the existence of the equilibrium point and local asymptotic stability are inferred. For various orders of the given derivative, the numerical simulations are displayed. We use graphs to verify the obtained results. According to our main outcomes, finding lice infestations early is important for getting rid of them quickly and effectively and lowering the risk of getting them again. These findings were used to test how well treatments for head lice infestations work. In the context of human disease, the results of this research highlight the relevance of projected derivative and method in the analysis and behavior of diverse mathematical models that are defined by differential equations.