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

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  • Qureshi, Sania
  • Yusuf, Abdullahi

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.

Suggested Citation

  • Qureshi, Sania & Yusuf, Abdullahi, 2019. "Mathematical modeling for the impacts of deforestation on wildlife species using Caputo differential operator," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 32-40.
    • Handle: RePEc:eee:chsofr:v:126:y:2019:i:c:p:32-40
    DOI: 10.1016/j.chaos.2019.05.037
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    References listed on IDEAS

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    4. Qureshi, Sania & Yusuf, Abdullahi, 2019. "Modeling chickenpox disease with fractional derivatives: From caputo to atangana-baleanu," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 111-118.
    5. Qureshi, Sania & Atangana, Abdon, 2019. "Mathematical analysis of dengue fever outbreak by novel fractional operators with field data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    6. Altaf Khan, Muhammad & Ullah, Saif & Farooq, Muhammad, 2018. "A new fractional model for tuberculosis with relapse via Atangana–Baleanu derivative," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 227-238.
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    Cited by:

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    7. Owolabi, Kolade M., 2020. "High-dimensional spatial patterns in fractional reaction-diffusion system arising in biology," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    8. Qureshi, Sania & Aziz, Shaheen, 2020. "Fractional modeling for a chemical kinetic reaction in a batch reactor via nonlocal operator with power law kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    9. Rubayyi T. Alqahtani & Abdullahi Yusuf & Ravi P. Agarwal, 2021. "Mathematical Analysis of Oxygen Uptake Rate in Continuous Process under Caputo Derivative," Mathematics, MDPI, vol. 9(6), pages 1-19, March.
    10. Yusuf, Abdullahi & Qureshi, Sania & Feroz Shah, Syed, 2020. "Mathematical analysis for an autonomous financial dynamical system via classical and modern fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    11. Lu, D. & Osman, M.S. & Khater, M.M.A. & Attia, R.A.M. & Baleanu, D., 2020. "Analytical and numerical simulations for the kinetics of phase separation in iron (Fe–Cr–X (X=Mo,Cu)) based on ternary alloys," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    12. Sekerci, Yadigar, 2020. "Climate change effects on fractional order prey-predator model," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).

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