IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v122y2019icp17-24.html

A new fractional analysis on the polluted lakes system

Author

Listed:
  • BİLDİK, Necdet
  • DENİZ, Sinan

Abstract

In this paper, we use Atangana–Baleanu derivative which is defined with the Mittag–Leffler function and has all the properties of a classical fractional derivative for solving the system of fractional differential equations. The classical model of polluted lakes system is modified by using the concept of fractional differentiation with nonsingular and nonlocal fading memory. The new numerical scheme recommended by Toufik and Atangana is used to analyze the modified model of polluted lakes system. Some numerical illustrations are presented to show the effect of the new fractional differentiation.

Suggested Citation

  • BİLDİK, Necdet & DENİZ, Sinan, 2019. "A new fractional analysis on the polluted lakes system," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 17-24.
    • Handle: RePEc:eee:chsofr:v:122:y:2019:i:c:p:17-24
    DOI: 10.1016/j.chaos.2019.02.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077918308427
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2019.02.001?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. Alkahtani, Badr Saad T., 2016. "Chua's circuit model with Atangana–Baleanu derivative with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 547-551.
    2. Atangana, Abdon & Koca, Ilknur, 2016. "Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 447-454.
    3. Algahtani, Obaid Jefain Julaighim, 2016. "Comparing the Atangana–Baleanu and Caputo–Fabrizio derivative with fractional order: Allen Cahn model," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 552-559.
    4. Brahim Benhammouda & Hector Vazquez-Leal & Luis Hernandez-Martinez, 2014. "Modified Differential Transform Method for Solving the Model of Pollution for a System of Lakes," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-12, September.
    Full references (including those not matched with items on IDEAS)

    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. 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).
    2. Alkahtani, Badr Saad T., 2018. "Numerical analysis of dissipative system with noise model with the Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 239-248.
    3. Jahanshahi, S. & Babolian, E. & Torres, D.F.M. & Vahidi, A.R., 2017. "A fractional Gauss–Jacobi quadrature rule for approximating fractional integrals and derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 295-304.
    4. Koca, Ilknur, 2018. "Efficient numerical approach for solving fractional partial differential equations with non-singular kernel derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 278-286.
    5. Debbouche, Amar & Antonov, Valery, 2017. "Approximate controllability of semilinear Hilfer fractional differential inclusions with impulsive control inclusion conditions in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 140-148.
    6. Owolabi, Kolade M. & Atangana, Abdon, 2017. "Numerical approximation of nonlinear fractional parabolic differential equations with Caputo–Fabrizio derivative in Riemann–Liouville sense," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 171-179.
    7. Hammad, Hasanen A. & Alshehri, Maryam G., 2024. "Application of the Mittag-Leffler kernel in stochastic differential systems for approximating the controllability of nonlocal fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    8. Dineshkumar, C. & Udhayakumar, R. & Vijayakumar, V. & Nisar, Kottakkaran Sooppy & Shukla, Anurag, 2022. "A note concerning to approximate controllability of Atangana-Baleanu fractional neutral stochastic systems with infinite delay," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    9. Sheikh, Nadeem Ahmad & Ali, Farhad & Khan, Ilyas & Gohar, Madeha, 2018. "A theoretical study on the performance of a solar collector using CeO2 and Al2O3 water based nanofluids with inclined plate: Atangana–Baleanu fractional model," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 135-142.
    10. Aimene, D. & Baleanu, D. & Seba, D., 2019. "Controllability of semilinear impulsive Atangana-Baleanu fractional differential equations with delay," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 51-57.
    11. Hashemi, M.S. & Atangana, A. & Hajikhah, S., 2020. "Solving fractional pantograph delay equations by an effective computational method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 295-305.
    12. Jiang, Jingfei & Chen, Huatao & Guirao, Juan L.G. & Cao, Dengqing, 2019. "Existence of the solution and stability for a class of variable fractional order differential systems," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 269-274.
    13. Hassan, Waqar Ul & Shabbir, Khurram & Zeeshan, Ahmed & Ellahi, Rahmat, 2025. "Regression analysis for thermal transport of fractional-order magnetohydrodynamic Maxwell fluid flow under the influence of chemical reaction using integrated machine learning approach," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    14. Peng, Li & Zhou, Yong & Debbouche, Amar, 2019. "Approximation techniques of optimal control problems for fractional dynamic systems in separable Hilbert spaces," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 234-241.
    15. Balcı, Ercan & Öztürk, İlhan & Kartal, Senol, 2019. "Dynamical behaviour of fractional order tumor model with Caputo and conformable fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 43-51.
    16. Yavuz, Mehmet & Bonyah, Ebenezer, 2019. "New approaches to the fractional dynamics of schistosomiasis disease model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 373-393.
    17. Sun, HongGuang & Hao, Xiaoxiao & Zhang, Yong & Baleanu, Dumitru, 2017. "Relaxation and diffusion models with non-singular kernels," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 590-596.
    18. Naik, Parvaiz Ahmad & Zu, Jian & Owolabi, Kolade M., 2020. "Modeling the mechanics of viral kinetics under immune control during primary infection of HIV-1 with treatment in fractional order," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    19. Atangana, Abdon, 2018. "Blind in a commutative world: Simple illustrations with functions and chaotic attractors," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 347-363.
    20. Fendzi-Donfack, Emmanuel & Kenfack-Jiotsa, Aurélien, 2023. "Extended Fan’s sub-ODE technique and its application to a fractional nonlinear coupled network including multicomponents — LC blocks," Chaos, Solitons & Fractals, Elsevier, vol. 177(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:122:y:2019:i:c:p:17-24. 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.