IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v157y2022ics096007792200159x.html
   My bibliography  Save this article

Stability of a time fractional advection-diffusion system

Author

Listed:
  • Arfaoui, Hassen
  • Ben Makhlouf, Abdellatif

Abstract

In this paper, we consider a one dimensional advection-diffusion system in Caputo fractional order derivative. Using a Fourier decomposition and the Mittag-Leffler Function (MLF), we prove a new stability results for the solution of a such system. Numerical experiments were carried out at the end of this work to confirm the theoretical results obtained.

Suggested Citation

  • Arfaoui, Hassen & Ben Makhlouf, Abdellatif, 2022. "Stability of a time fractional advection-diffusion system," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s096007792200159x
    DOI: 10.1016/j.chaos.2022.111949
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007792200159X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.111949?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. Ghanbari, Behzad & Günerhan, Hatıra & Srivastava, H.M., 2020. "An application of the Atangana-Baleanu fractional derivative in mathematical biology: A three-species predator-prey model," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    2. Salahshour, Soheil & Ahmadian, Ali & Allahviranloo, Tofigh, 2021. "A new fractional dynamic cobweb model based on nonsingular kernel derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    3. Singh, Jagdev & Kumar, Devendra & Hammouch, Zakia & Atangana, Abdon, 2018. "A fractional epidemiological model for computer viruses pertaining to a new fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 504-515.
    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. Arfaoui, Hassen & Ben Makhlouf, Abdellatif, 2022. "Stability of a fractional advection–diffusion system with conformable derivative," Chaos, Solitons & Fractals, Elsevier, vol. 164(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. Arfaoui, Hassen & Ben Makhlouf, Abdellatif, 2022. "Stability of a fractional advection–diffusion system with conformable derivative," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Prakash, Amit & Kaur, Hardish, 2021. "Analysis and numerical simulation of fractional Biswas–Milovic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 298-315.
    3. Ravichandran, C. & Logeswari, K. & Panda, Sumati Kumari & Nisar, Kottakkaran Sooppy, 2020. "On new approach of fractional derivative by Mittag-Leffler kernel to neutral integro-differential systems with impulsive conditions," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    4. Solís-Pérez, J.E. & Gómez-Aguilar, J.F. & Atangana, A., 2018. "Novel numerical method for solving variable-order fractional differential equations with power, exponential and Mittag-Leffler laws," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 175-185.
    5. ur Rahman, Ghaus & Agarwal, Ravi P. & Din, Qamar, 2019. "Mathematical analysis of giving up smoking model via harmonic mean type incidence rate," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 128-148.
    6. 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.
    7. Ghalib, M. Mansha & Zafar, Azhar A. & Riaz, M. Bilal & Hammouch, Z. & Shabbir, Khurram, 2020. "Analytical approach for the steady MHD conjugate viscous fluid flow in a porous medium with nonsingular fractional derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    8. Rahman, Mati ur & Arfan, Muhammad & Shah, Kamal & Gómez-Aguilar, J.F., 2020. "Investigating a nonlinear dynamical model of COVID-19 disease under fuzzy caputo, random and ABC fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    9. Owolabi, Kolade M., 2018. "Numerical patterns in reaction–diffusion system with the Caputo and Atangana–Baleanu fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 160-169.
    10. Boukhouima, Adnane & Hattaf, Khalid & Lotfi, El Mehdi & Mahrouf, Marouane & Torres, Delfim F.M. & Yousfi, Noura, 2020. "Lyapunov functions for fractional-order systems in biology: Methods and applications," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    11. Hari Mohan Srivastava & Khaled M. Saad, 2020. "A Comparative Study of the Fractional-Order Clock Chemical Model," Mathematics, MDPI, vol. 8(9), pages 1-14, August.
    12. Deniz, Sinan, 2021. "Optimal perturbation iteration method for solving fractional FitzHugh-Nagumo equation," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    13. Hassouna, M. & Ouhadan, A. & El Kinani, E.H., 2018. "On the solution of fractional order SIS epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 168-174.
    14. Aliyu, Aliyu Isa & Inc, Mustafa & Yusuf, Abdullahi & Baleanu, Dumitru, 2018. "A fractional model of vertical transmission and cure of vector-borne diseases pertaining to the Atangana–Baleanu fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 268-277.
    15. Bonyah, Ebenezer & Gómez-Aguilar, J.F. & Adu, Augustina, 2018. "Stability analysis and optimal control of a fractional human African trypanosomiasis model," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 150-160.
    16. Djilali, Salih & Ghanbari, Behzad & Bentout, Soufiane & Mezouaghi, Abdelheq, 2020. "Turing-Hopf bifurcation in a diffusive mussel-algae model with time-fractional-order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    17. Marasi, H.R. & Derakhshan, M.H., 2023. "Numerical simulation of time variable fractional order mobile–immobile advection–dispersion model based on an efficient hybrid numerical method with stability and convergence analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 368-389.
    18. 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).
    19. Nazir, Aqsa & Ahmed, Naveed & Khan, Umar & Mohyud-din, Syed Tauseef, 2020. "On stability of improved conformable model for studying the dynamics of a malnutrition community," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    20. Abdeljawad, Thabet & Atangana, Abdon & Gómez-Aguilar, J.F. & Jarad, Fahd, 2019. "On a more general fractional integration by parts formulae and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(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:157:y:2022:i:c:s096007792200159x. 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.