IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v132y2020ics0960077919305430.html
   My bibliography  Save this article

Stability and Lyapunov functions for systems with Atangana–Baleanu Caputo derivative: An HIV/AIDS epidemic model

Author

Listed:
  • Taneco-Hernández, Marco Antonio
  • Vargas-De-León, Cruz

Abstract

In this paper, we derive extensions of classical Lyapunov and Chetaev instability theorems and LaSalle’s invariance principle to the case of Atangana–Baleanu derivative in the Caputo sence. Moreover, we get some results to estimates fractional derivatives of quadratic and Volterra–type Lyapunov functions when γ ∈ (0, 1). Finally, we present rigorous proofs about the complete classification for global dynamics of an HIV/AIDS epidemic model with Atangana–Baleanu Caputo derivative (Chaos, Solitons and Fractals 126 (2019) 41–49).

Suggested Citation

  • Taneco-Hernández, Marco Antonio & Vargas-De-León, Cruz, 2020. "Stability and Lyapunov functions for systems with Atangana–Baleanu Caputo derivative: An HIV/AIDS epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    • Handle: RePEc:eee:chsofr:v:132:y:2020:i:c:s0960077919305430
    DOI: 10.1016/j.chaos.2019.109586
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077919305430
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2019.109586?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. Gallegos, Javier A. & Duarte-Mermoud, Manuel A., 2016. "On the Lyapunov theory for fractional order systems," Applied Mathematics and Computation, Elsevier, vol. 287, pages 161-170.
    2. 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.
    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. Gilberto Gonzalez-Parra & Abraham J. Arenas, 2021. "Nonlinear Dynamics of the Introduction of a New SARS-CoV-2 Variant with Different Infectiousness," Mathematics, MDPI, vol. 9(13), pages 1-22, July.
    2. Oscar Martínez-Fuentes & Fidel Meléndez-Vázquez & Guillermo Fernández-Anaya & José Francisco Gómez-Aguilar, 2021. "Analysis of Fractional-Order Nonlinear Dynamic Systems with General Analytic Kernels: Lyapunov Stability and Inequalities," Mathematics, MDPI, vol. 9(17), pages 1-29, August.

    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. Pritam, Kocherlakota Satya & Sugandha, & Mathur, Trilok & Agarwal, Shivi, 2021. "Underlying dynamics of crime transmission with memory," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    2. Bukhari, Ayaz Hussain & Raja, Muhammad Asif Zahoor & Shoaib, Muhammad & Kiani, Adiqa Kausar, 2022. "Fractional order Lorenz based physics informed SARFIMA-NARX model to monitor and mitigate megacities air pollution," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    3. 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.
    4. Mishra, A.M. & Purohit, S.D. & Owolabi, K.M. & Sharma, Y.D., 2020. "A nonlinear epidemiological model considering asymptotic and quarantine classes for SARS CoV-2 virus," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    5. 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).
    6. Ishtiaq Ali & Sami Ullah Khan, 2023. "A Dynamic Competition Analysis of Stochastic Fractional Differential Equation Arising in Finance via Pseudospectral Method," Mathematics, MDPI, vol. 11(6), pages 1-16, March.
    7. Bei Zhang & Yonghui Xia & Lijuan Zhu & Haidong Liu & Longfei Gu, 2019. "Global Stability of Fractional Order Coupled Systems with Impulses via a Graphic Approach," Mathematics, MDPI, vol. 7(8), pages 1-10, August.
    8. Ravi Kanth, A.S.V. & Devi, Sangeeta, 2021. "A practical numerical approach to solve a fractional Lotka–Volterra population model with non-singular and singular kernels," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    9. Zhang, Zhe & Wang, Yaonan & Zhang, Jing & Ai, Zhaoyang & Liu, Feng, 2022. "Novel stability results of multivariable fractional-order system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    10. Goyal, Manish & Baskonus, Haci Mehmet & Prakash, Amit, 2020. "Regarding new positive, bounded and convergent numerical solution of nonlinear time fractional HIV/AIDS transmission model," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    11. Naik, Parvaiz Ahmad & Zu, Jian & Owolabi, Kolade M., 2020. "Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    12. Okposo, Newton I. & Adewole, Matthew O. & Okposo, Emamuzo N. & Ojarikre, Herietta I. & Abdullah, Farah A., 2021. "A mathematical study on a fractional COVID-19 transmission model within the framework of nonsingular and nonlocal kernel," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    13. Kolebaje, Olusola & Popoola, Oyebola & Khan, Muhammad Altaf & Oyewande, Oluwole, 2020. "An epidemiological approach to insurgent population modeling with the Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    14. Chenhui Wang, 2016. "Adaptive Fuzzy Control for Uncertain Fractional-Order Financial Chaotic Systems Subjected to Input Saturation," PLOS ONE, Public Library of Science, vol. 11(10), pages 1-17, October.
    15. Maike A. F. dos Santos, 2019. "Mittag–Leffler Memory Kernel in Lévy Flights," Mathematics, MDPI, vol. 7(9), pages 1-13, August.
    16. Bhatter, Sanjay & Mathur, Amit & Kumar, Devendra & Nisar, Kottakkaran Sooppy & Singh, Jagdev, 2020. "Fractional modified Kawahara equation with Mittag–Leffler law," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    17. Wu, Guo-Cheng & Baleanu, Dumitru & Luo, Wei-Hua, 2017. "Lyapunov functions for Riemann–Liouville-like fractional difference equations," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 228-236.
    18. Yang, Xujun & Li, Chuandong & Huang, Tingwen & Song, Qiankun, 2017. "Mittag–Leffler stability analysis of nonlinear fractional-order systems with impulses," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 416-422.
    19. Yousefpour, Amin & Jahanshahi, Hadi & Bekiros, Stelios, 2020. "Optimal policies for control of the novel coronavirus disease (COVID-19) outbreak," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    20. Wei, Q. & Yang, S. & Zhou, H.W. & Zhang, S.Q. & Li, X.N. & Hou, W., 2021. "Fractional diffusion models for radionuclide anomalous transport in geological repository systems," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

    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:132:y:2020:i:c:s0960077919305430. 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.