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

By Sania Qureshi, Abdullahi Yusuf. Chaos, Solitons & Fractals, 2019

82 citations recorded by the source corpus.

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 + τ , 2 ) , where τ 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 τ and parameters of the model itself are used during the required numerical simulations.

Subfields: Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/8914af2a34d833af542440191e00d53223d41d1f