IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v133y2020ics0960077920300230.html
   My bibliography  Save this article

Atangana-Baleanu fractional framework of reproducing kernel technique in solving fractional population dynamics system

Author

Listed:
  • Hasan, Shatha
  • El-Ajou, Ahmad
  • Hadid, Samir
  • Al-Smadi, Mohammed
  • Momani, Shaher

Abstract

In this article, a class of population growth model, the fractional nonlinear logistic system, is studied analytically and numerically. This model is investigated by means of Atangana-Baleanu fractional derivative with a non-local smooth kernel in Sobolev space. Existence and uniqueness theorem for the fractional logistic equation is provided based on the fixed-point theory. In this orientation, two numerical techniques are implemented to obtain the approximate solutions; the reproducing-kernel algorithm is based on the Schmidt orthogonalization process to construct a complete normal basis, while the successive substitution algorithm is based on an appropriate iterative scheme. Convergence analysis associated with the suggested approaches is provided to demonstrate the applicability theoretically. The impact of the fractional derivative on population growth is discussed by a class of nonlinear logistical models using the derivatives of Caputo, Caputo-Fabrizio, and Atangana-Baleanu. Using specific examples, numerical simulations are presented in tables and graphs to show the effect of the fractional operator on the population curve as. The present results confirm the theoretical predictions and depict that the suggested schemes are highly convenient, quite effective and practically simplify computational time.

Suggested Citation

  • Hasan, Shatha & El-Ajou, Ahmad & Hadid, Samir & Al-Smadi, Mohammed & Momani, Shaher, 2020. "Atangana-Baleanu fractional framework of reproducing kernel technique in solving fractional population dynamics system," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    • Handle: RePEc:eee:chsofr:v:133:y:2020:i:c:s0960077920300230
    DOI: 10.1016/j.chaos.2020.109624
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920300230
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.109624?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 search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Atangana, Abdon, 2016. "On the new fractional derivative and application to nonlinear Fisher’s reaction–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 948-956.
    3. 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.
    4. N. H. Sweilam & M. M. Khader & A. M. S. Mahdy, 2012. "Numerical Studies for Fractional-Order Logistic Differential Equation with Two Different Delays," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, September.
    5. Al-Smadi, Mohammed & Arqub, Omar Abu, 2019. "Computational algorithm for solving fredholm time-fractional partial integrodifferential equations of dirichlet functions type with error estimates," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 280-294.
    6. Al-Smadi, Mohammed & Arqub, Omar Abu & Shawagfeh, Nabil & Momani, Shaher, 2016. "Numerical investigations for systems of second-order periodic boundary value problems using reproducing kernel method," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 137-148.
    7. Abu Arqub, Omar & Al-Smadi, Mohammed, 2020. "An adaptive numerical approach for the solutions of fractional advection–diffusion and dispersion equations in singular case under Riesz’s derivative operator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    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. Hussam Aljarrah & Mohammad Alaroud & Anuar Ishak & Maslina Darus, 2022. "Approximate Solution of Nonlinear Time-Fractional PDEs by Laplace Residual Power Series Method," Mathematics, MDPI, vol. 10(12), pages 1-16, June.
    2. Li, Yi Xia & Alshehri, Maryam G. & Algehyne, Ebrahem A. & Ali, Aatif & Khan, Muhammad Altaf & Muhammad, Taseer & Islam, Saeed, 2021. "Fractional study of Huanglongbing model with singular and non- singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    3. Fouladi, Somayeh & Dahaghin, Mohammad Shafi, 2022. "Numerical investigation of the variable-order fractional Sobolev equation with non-singular Mittag–Leffler kernel by finite difference and local discontinuous Galerkin methods," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    4. Muhammad Imran Liaqat & Ali Akgül & Hanaa Abu-Zinadah, 2023. "Analytical Investigation of Some Time-Fractional Black–Scholes Models by the Aboodh Residual Power Series Method," Mathematics, MDPI, vol. 11(2), pages 1-19, January.
    5. Laila F. Seddek & Essam R. El-Zahar & Jae Dong Chung & Nehad Ali Shah, 2023. "A Novel Approach to Solving Fractional-Order Kolmogorov and Rosenau–Hyman Models through the q-Homotopy Analysis Transform Method," Mathematics, MDPI, vol. 11(6), pages 1-11, March.
    6. Attia, Nourhane & Akgül, Ali & Seba, Djamila & Nour, Abdelkader, 2020. "An efficient numerical technique for a biological population model of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    7. Hussam Aljarrah & Mohammad Alaroud & Anuar Ishak & Maslina Darus, 2021. "Adaptation of Residual-Error Series Algorithm to Handle Fractional System of Partial Differential Equations," Mathematics, MDPI, vol. 9(22), pages 1-17, November.
    8. Hasan, Shatha & Al-Smadi, Mohammed & El-Ajou, Ahmad & Momani, Shaher & Hadid, Samir & Al-Zhour, Zeyad, 2021. "Numerical approach in the Hilbert space to solve a fuzzy Atangana-Baleanu fractional hybrid system," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

    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. Djennadi, Smina & Shawagfeh, Nabil & Abu Arqub, Omar, 2021. "A fractional Tikhonov regularization method for an inverse backward and source problems in the time-space fractional diffusion equations," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    2. Al-Smadi, Mohammed & Arqub, Omar Abu & Zeidan, Dia, 2021. "Fuzzy fractional differential equations under the Mittag-Leffler kernel differential operator of the ABC approach: Theorems and applications," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    3. Omar Abu Arqub & Mohamed S. Osman & Abdel-Haleem Abdel-Aty & Abdel-Baset A. Mohamed & Shaher Momani, 2020. "A Numerical Algorithm for the Solutions of ABC Singular Lane–Emden Type Models Arising in Astrophysics Using Reproducing Kernel Discretization Method," Mathematics, MDPI, vol. 8(6), pages 1-15, June.
    4. Yadav, Swati & Pandey, Rajesh K., 2020. "Numerical approximation of fractional burgers equation with Atangana–Baleanu derivative in Caputo sense," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    5. Arqub, Omar Abu & Maayah, Banan, 2019. "Fitted fractional reproducing kernel algorithm for the numerical solutions of ABC – Fractional Volterra integro-differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 394-402.
    6. Abu Arqub, Omar & Maayah, Banan, 2019. "Modulation of reproducing kernel Hilbert space method for numerical solutions of Riccati and Bernoulli equations in the Atangana-Baleanu fractional sense," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 163-170.
    7. 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).
    8. Mathale, D. & Doungmo Goufo, Emile F. & Khumalo, M., 2020. "Coexistence of multi-scroll chaotic attractors for fractional systems with exponential law and non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    9. Saad, Khaled M. & Gómez-Aguilar, J.F., 2018. "Analysis of reaction–diffusion system via a new fractional derivative with non-singular kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 703-716.
    10. Mohammed, Pshtiwan Othman & Kürt, Cemaliye & Abdeljawad, Thabet, 2022. "Bivariate discrete Mittag-Leffler functions with associated discrete fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    11. Amiri, Pari & Afshari, Hojjat, 2022. "Common fixed point results for multi-valued mappings in complex-valued double controlled metric spaces and their applications to the existence of solution of fractional integral inclusion systems," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    12. Zúñiga-Aguilar, C.J. & Gómez-Aguilar, J.F. & Escobar-Jiménez, R.F. & Romero-Ugalde, H.M., 2019. "A novel method to solve variable-order fractional delay differential equations based in lagrange interpolations," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 266-282.
    13. Mallika Arjunan, M. & Hamiaz, A. & Kavitha, V., 2021. "Existence results for Atangana-Baleanu fractional neutral integro-differential systems with infinite delay through sectorial operators," Chaos, Solitons & Fractals, Elsevier, vol. 149(C).
    14. Coronel-Escamilla, A. & Gómez-Aguilar, J.F. & López-López, M.G. & Alvarado-Martínez, V.M. & Guerrero-Ramírez, G.V., 2016. "Triple pendulum model involving fractional derivatives with different kernels," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 248-261.
    15. Ali, Farhad & Murtaza, Saqib & Sheikh, Nadeem Ahmad & Khan, Ilyas, 2019. "Heat transfer analysis of generalized Jeffery nanofluid in a rotating frame: Atangana–Balaenu and Caputo–Fabrizio fractional models," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 1-15.
    16. Fetecau, C. & Zafar, A.A. & Vieru, D. & Awrejcewicz, J., 2020. "Hydromagnetic flow over a moving plate of second grade fluids with time fractional derivatives having non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    17. 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.
    18. 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).
    19. 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.
    20. 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.

    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:133:y:2020:i:c:s0960077920300230. 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.