Mathematical modeling for the impacts of deforestation on wildlife species using Caputo differential operator

Abstract

This research study shows the impacts of deforestation on wildlife species using a newly proposed four dimensional nonlinear mathematical model based upon fractional-order ordinary differential equations. Being a nonlinear model, some theorems using fixed point theory have been proved showing the existence and uniqueness properties for the solution of the fractional-order model. Using an explicit version of Adams-Bashforth-Moulton method devised for the fractional-order ordinary differential equations with convergence order p = min(1 + tau, 2), where tau is the order of the differential equations used in the model; some numerical simulations in the form of graphical illustrations have been carried out depicting the better performance of the fractional-order model for being capable enough to capture all the history information of the system under consideration which is a phenomenon not found in the classical (integer-order) differential equations. Varying values for both the fractional-order parameter tau and parameters of the model itself are used during the required numerical simulations. (C) 2019 Elsevier Ltd. All rights reserved.