Fractional Derivatives with the Power-Law and the Mittaga??Leffler Kernel Applied to the Nonlinear Baggsa??Freedman Model

摘要

This paper considers the Freedman model using the Liouvillea??Caputo fractional-order derivative and the fractional-order derivative with Mittaga??Leffler kernel in the Liouvillea??Caputo sense. Alternative solutions via Laplace transform, Sumudua??Picard and Adamsa??Moulton rules were obtained. We prove the uniqueness and existence of the solutions for the alternative model. Numerical simulations for the prediction and interaction between a unilingual and a bilingual population were obtained for different values of the fractional order.