IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v148y2021ics096007792100391x.html
   My bibliography  Save this article

Fractional study of Huanglongbing model with singular and non- singular kernel

Author

Listed:
  • Li, Yi Xia
  • Alshehri, Maryam G.
  • Algehyne, Ebrahem A.
  • Ali, Aatif
  • Khan, Muhammad Altaf
  • Muhammad, Taseer
  • Islam, Saeed

Abstract

The disease of citrus is Huanglongbing (HLB), a Chinese name meaning yellow shoot disease and in English-speaking countries referred as a citrus greening threatening the citrus industries worldwide. Citrus greening associated with ’Candidatus Liberibacter asiaticus’ (CLas), is the most devastating disease spread through the infected citrus trees and the major insect vector, the infected citrus psyllid (Diaphorina citri). A fractional-order compartmental model in Caputo and Atangana–Baleanu sense is consider to study the dynamical aspects of HLB among citrus trees and Asian citrus psyllid (ACP). We computed a basic reproduction number and present a detailed theoretical analysis including solution positivity and the stability of disease-free equilibrium of the Caputo fractional model. Numerical simulations are conducted for both Caputo and Atangana–Baleanu operators. The numerical results of Caputo model suggest that the infection and removal rate impacts impressively on the severity of the HLB. Moreover, for different values of the fractional derivative suggest the infection minimization and possibly the control for the disease. While simulating the model using both the operators, the results captured are are better and may be useful in further research of the proposed model. We conclude that, the Atangana–Baleanu operator is more effective and prominent biologically as compared to the Caputo derivative for the proposed problem.

Suggested Citation

  • 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).
  • Handle: RePEc:eee:chsofr:v:148:y:2021:i:c:s096007792100391x
    DOI: 10.1016/j.chaos.2021.111037
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007792100391X
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2021.111037?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. Ahmed, E. & Elgazzar, A.S., 2007. "On fractional order differential equations model for nonlocal epidemics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(2), pages 607-614.
    2. 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).
    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. Gao, Shujing & Yu, Dan & Meng, Xinzhu & Zhang, Fumin, 2018. "Global dynamics of a stage-structured Huanglongbing model with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 60-67.
    5. Dubey, Ved Prakash & Dubey, Sarvesh & Kumar, Devendra & Singh, Jagdev, 2021. "A computational study of fractional model of atmospheric dynamics of carbon dioxide gas," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    6. Shujing Gao & Lei Luo & Shuixian Yan & Xinzhu Meng, 2018. "Dynamical Behavior of a Novel Impulsive Switching Model for HLB with Seasonal Fluctuations," Complexity, Hindawi, vol. 2018, pages 1-11, July.
    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. Xu, Changjin & Alhejaili, Weaam & Saifullah, Sayed & Khan, Arshad & Khan, Javed & El-Shorbagy, M.A., 2022. "Analysis of Huanglongbing disease model with a novel fractional piecewise approach," Chaos, Solitons & Fractals, Elsevier, vol. 161(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. Al-khedhairi, A. & Matouk, A.E. & Khan, I., 2019. "Chaotic dynamics and chaos control for the fractional-order geomagnetic field model," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 390-401.
    2. Akgül, Esra Karatas & Akgül, Ali & Yavuz, Mehmet, 2021. "New Illustrative Applications of Integral Transforms to Financial Models with Different Fractional Derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    3. Miao Ouyang & Yongping Zhang, 2019. "Julia Sets and Their Control of Discrete Fractional SIRS Models," Complexity, Hindawi, vol. 2019, pages 1-10, June.
    4. Pratap, A. & Raja, R. & Cao, J. & Lim, C.P. & Bagdasar, O., 2019. "Stability and pinning synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous activations," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 241-260.
    5. 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).
    6. Gafiychuk, V. & Datsko, B. & Meleshko, V., 2008. "Analysis of fractional order Bonhoeffer–van der Pol oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 418-424.
    7. 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.
    8. 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.
    9. Ricardo Almeida & Agnieszka B. Malinowska & Tatiana Odzijewicz, 2019. "Optimal Leader–Follower Control for the Fractional Opinion Formation Model," Journal of Optimization Theory and Applications, Springer, vol. 182(3), pages 1171-1185, September.
    10. Ilhan, Esin & Veeresha, P. & Baskonus, Haci Mehmet, 2021. "Fractional approach for a mathematical model of atmospheric dynamics of CO2 gas with an efficient method," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    11. 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.
    12. Jiale Sheng & Wei Jiang & Denghao Pang & Sen Wang, 2020. "Controllability of Nonlinear Fractional Dynamical Systems with a Mittag–Leffler Kernel," Mathematics, MDPI, vol. 8(12), pages 1-10, December.
    13. 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.
    14. Owolabi, Kolade M. & Atangana, Abdon, 2019. "Mathematical analysis and computational experiments for an epidemic system with nonlocal and nonsingular derivative," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 41-49.
    15. 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).
    16. Kumar, Sachin & Pandey, Prashant, 2020. "Quasi wavelet numerical approach of non-linear reaction diffusion and integro reaction-diffusion equation with Atangana–Baleanu time fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    17. Silva, Cristiana J. & Torres, Delfim F.M., 2019. "Stability of a fractional HIV/AIDS model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 164(C), pages 180-190.
    18. Kumar, Sachin & Cao, Jinde & Abdel-Aty, Mahmoud, 2020. "A novel mathematical approach of COVID-19 with non-singular fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    19. Majee, Suvankar & Jana, Soovoojeet & Das, Dhiraj Kumar & Kar, T.K., 2022. "Global dynamics of a fractional-order HFMD model incorporating optimal treatment and stochastic stability," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    20. 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.

    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:148:y:2021:i:c:s096007792100391x. 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.