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

Sania Qureshi and Abdullahi Yusuf

Chaos, Solitons & Fractals, 2019, vol. 126, issue C, 32-40

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.

Keywords: Wildlife; Global warming; Fixed point theory; Numerical simulation (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (13)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:126:y:2019:i:c:p:32-40

DOI: 10.1016/j.chaos.2019.05.037

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