IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v126y2019icp32-40.html

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077919302024
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2019.05.037?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Ramos, Higinio & Singh, Gurjinder, 2017. "A tenth order A-stable two-step hybrid block method for solving initial value problems of ODEs," Applied Mathematics and Computation, Elsevier, vol. 310(C), pages 75-88.
    2. Abu Arqub, Omar & Al-Smadi, Mohammed, 2018. "Atangana–Baleanu fractional approach to the solutions of Bagley–Torvik and Painlevé equations in Hilbert space," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 161-167.
    3. 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.
    4. Atangana, Abdon & Qureshi, Sania, 2019. "Modeling attractors of chaotic dynamical systems with fractal–fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 320-337.
    5. Misra, A.K. & Lata, Kusum, 2013. "Modeling the effect of time delay on the conservation of forestry biomass," Chaos, Solitons & Fractals, Elsevier, vol. 46(C), pages 1-11.
    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.
    7. 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).
    8. Ullah, Saif & Altaf Khan, Muhammad & Farooq, Muhammad, 2018. "A fractional model for the dynamics of TB virus," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 63-71.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Owolabi, Kolade M., 2020. "High-dimensional spatial patterns in fractional reaction-diffusion system arising in biology," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    2. Owolabi, Kolade M. & Pindza, Edson & Atangana, Abdon, 2021. "Analysis and pattern formation scenarios in the superdiffusive system of predation described with Caputo operator," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. 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).
    4. Mustapha, Umar Tasiu & Qureshi, Sania & Yusuf, Abdullahi & Hincal, Evren, 2020. "Fractional modeling for the spread of Hookworm infection under Caputo operator," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    5. Qureshi, Sania & Memon, Zaib-un-Nisa, 2020. "Monotonically decreasing behavior of measles epidemic well captured by Atangana–Baleanu–Caputo fractional operator under real measles data of Pakistan," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    6. 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).
    7. Qureshi, Sania, 2020. "Real life application of Caputo fractional derivative for measles epidemiological autonomous dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    8. Kumar, Pushpendra & Erturk, Vedat Suat, 2021. "Environmental persistence influences infection dynamics for a butterfly pathogen via new generalised Caputo type fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    9. Farman, Muhammad & Jamil, Khadija & Xu, Changjin & Nisar, Kottakkaran Sooppy & Amjad, Ayesha, 2025. "Fractional order forestry resource conservation model featuring chaos control and simulations for toxin activity and human-caused fire through modified ABC operator," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 227(C), pages 282-302.
    10. Sekerci, Yadigar, 2020. "Climate change effects on fractional order prey-predator model," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    11. 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).
    12. Amouch, Mohamed & Karim, Noureddine, 2021. "Modeling the dynamic of COVID-19 with different types of transmissions," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    13. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Qureshi, Sania & Memon, Zaib-un-Nisa, 2020. "Monotonically decreasing behavior of measles epidemic well captured by Atangana–Baleanu–Caputo fractional operator under real measles data of Pakistan," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    2. Wang, Wanting & Khan, Muhammad Altaf & Fatmawati, & Kumam, P. & Thounthong, P., 2019. "A comparison study of bank data in fractional calculus," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 369-384.
    3. Li, Zhongfei & Liu, Zhuang & Khan, Muhammad Altaf, 2020. "Fractional investigation of bank data with fractal-fractional Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    4. Berhe, Hailay Weldegiorgis & Qureshi, Sania & Shaikh, Asif Ali, 2020. "Deterministic modeling of dysentery diarrhea epidemic under fractional Caputo differential operator via real statistical analysis," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    5. 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).
    6. Qureshi, Sania & Atangana, Abdon, 2020. "Fractal-fractional differentiation for the modeling and mathematical analysis of nonlinear diarrhea transmission dynamics under the use of real data," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    7. Atangana, Abdon & Qureshi, Sania, 2019. "Modeling attractors of chaotic dynamical systems with fractal–fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 320-337.
    8. Yadav, Ram Prasad & Renu Verma,, 2020. "A numerical simulation of fractional order mathematical modeling of COVID-19 disease in case of Wuhan China," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    9. Abro, Kashif Ali & Khan, Ilyas & Nisar, Kottakkaran Sooppy, 2019. "Novel technique of Atangana and Baleanu for heat dissipation in transmission line of electrical circuit," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 40-45.
    10. Verma, Lalchand & Meher, Ramakanta & Pandya, Darshak P., 2025. "Parameter estimation study of temporal fractional HIV/AIDS transmission model with fractal dimensions using real data in India," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 234(C), pages 135-150.
    11. Qureshi, Sania, 2020. "Periodic dynamics of rubella epidemic under standard and fractional Caputo operator with real data from Pakistan," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 151-165.
    12. 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.
    13. Sania Qureshi & Norodin A. Rangaig & Dumitru Baleanu, 2019. "New Numerical Aspects of Caputo-Fabrizio Fractional Derivative Operator," Mathematics, MDPI, vol. 7(4), pages 1-14, April.
    14. Akgül, Ali & Partohaghighi, Mohammad, 2022. "New fractional modelling and control analysis of the circumscribed self-excited spherical strange attractor," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    15. Mustapha, Umar Tasiu & Qureshi, Sania & Yusuf, Abdullahi & Hincal, Evren, 2020. "Fractional modeling for the spread of Hookworm infection under Caputo operator," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    16. El-Dessoky Ahmed, M.M. & Altaf Khan, Muhammad, 2020. "Modeling and analysis of the polluted lakes system with various fractional approaches," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    17. Qureshi, Sania, 2020. "Real life application of Caputo fractional derivative for measles epidemiological autonomous dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    18. Qureshi, Sania & Jan, Rashid, 2021. "Modeling of measles epidemic with optimized fractional order under Caputo differential operator," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    19. Chukwu, C.W. & Fatmawati, & Utoyo, M.I. & Setiawan, A. & Akanni, J.O., 2024. "Fractional model of HIV transmission on workplace productivity using real data from Indonesia," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 1089-1103.
    20. Rihan, F.A. & Rajivganthi, C, 2020. "Dynamics of fractional-order delay differential model of prey-predator system with Holling-type III and infection among predators," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:126:y:2019:i:c:p:32-40. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.