IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v136y2020ics0960077920302356.html
   My bibliography  Save this article

Dynamics of multi-pulse splitting process in one-dimensional Gray-Scott system with fractional order operator

Author

Listed:
  • Owolabi, Kolade M.
  • Karaagac, Berat

Abstract

In this paper, the dynamic process of pulse-splitting patterns is reported in fractional medium. In the classical Gray-Scott system, the integer-order derivative is replaced with the known Atangana-Baleanu fractional order derivative in the sense of Caputo. mathematical analysis such as the existence of stationary solutions for pulse-splitting process, existence and uniqueness of solutions for the fractional system are presented. The beauty of the work is further demonstrated by presenting numerical results for different values of γ in one dimensional space. We deduced from the numerical experiments that pulse-splitting patterns in both integer and noninteger order scenarios are almost the same.

Suggested Citation

  • Owolabi, Kolade M. & Karaagac, Berat, 2020. "Dynamics of multi-pulse splitting process in one-dimensional Gray-Scott system with fractional order operator," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
  • Handle: RePEc:eee:chsofr:v:136:y:2020:i:c:s0960077920302356
    DOI: 10.1016/j.chaos.2020.109835
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920302356
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2020.109835?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. 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.
    2. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    3. Owolabi, Kolade M. & Gómez-Aguilar, J.F., 2018. "Numerical simulations of multilingual competition dynamics with nonlocal derivative," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 175-182.
    4. 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.
    5. Karaagac, Berat, 2019. "A study on fractional Klein Gordon equation with non-local and non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 218-229.
    6. Owolabi, Kolade M., 2018. "Analysis and numerical simulation of multicomponent system with Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 127-134.
    7. Atangana, Abdon & Alqahtani, Rubayyi T., 2018. "New numerical method and application to Keller-Segel model with fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 14-21.
    8. Arshad, Sadia & Defterli, Ozlem & Baleanu, Dumitru, 2020. "A second order accurate approximation for fractional derivatives with singular and non-singular kernel applied to a HIV model," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    9. Owolabi, Kolade M., 2018. "Numerical patterns in system of integer and non-integer order derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 143-153.
    10. Atangana, Abdon, 2018. "Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 688-706.
    11. Atangana, Abdon & Gómez-Aguilar, J.F., 2018. "Fractional derivatives with no-index law property: Application to chaos and statistics," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 516-535.
    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. 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).
    2. Bukhari, Ayaz Hussain & Raja, Muhammad Asif Zahoor & Rafiq, Naila & Shoaib, Muhammad & Kiani, Adiqa Kausar & Shu, Chi-Min, 2022. "Design of intelligent computing networks for nonlinear chaotic fractional Rossler system," Chaos, Solitons & Fractals, Elsevier, vol. 157(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. Owolabi, Kolade M., 2019. "Mathematical modelling and analysis of love dynamics: A fractional approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 849-865.
    2. Owolabi, Kolade M. & Pindza, Edson, 2019. "Modeling and simulation of nonlinear dynamical system in the frame of nonlocal and non-singular derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 146-157.
    3. Morales-Delgado, V.F. & Gómez-Aguilar, J.F. & Saad, Khaled M. & Khan, Muhammad Altaf & Agarwal, P., 2019. "Analytic solution for oxygen diffusion from capillary to tissues involving external force effects: A fractional calculus approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 48-65.
    4. 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.
    5. Khan, Hasib & Gómez-Aguilar, J.F. & Khan, Aziz & Khan, Tahir Saeed, 2019. "Stability analysis for fractional order advection–reaction diffusion system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 737-751.
    6. 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.
    7. Karaagac, Berat, 2019. "Two step Adams Bashforth method for time fractional Tricomi equation with non-local and non-singular Kernel," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 234-241.
    8. Goufo, Emile F. Doungmo & Khumalo, M & Toudjeu, Ignace Tchangou & Yildirim, Ahmet, 2020. "Mathematical application of a non-local operator in language evolutionary theory," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    9. Karaagac, Berat, 2019. "A study on fractional Klein Gordon equation with non-local and non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 218-229.
    10. Hosseininia, M. & Heydari, M.H., 2019. "Meshfree moving least squares method for nonlinear variable-order time fractional 2D telegraph equation involving Mittag–Leffler non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 389-399.
    11. Ahmad, Shabir & Ullah, Aman & Arfan, Muhammad & Shah, Kamal, 2020. "On analysis of the fractional mathematical model of rotavirus epidemic with the effects of breastfeeding and vaccination under Atangana-Baleanu (AB) derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    12. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    13. Owolabi, Kolade M. & Hammouch, Zakia, 2019. "Spatiotemporal patterns in the Belousov–Zhabotinskii reaction systems with Atangana–Baleanu fractional order derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1072-1090.
    14. Al-khedhairi, A. & Elsadany, A.A. & Elsonbaty, A., 2019. "Modelling immune systems based on Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 25-39.
    15. 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.
    16. Ávalos-Ruiz, L.F. & Gómez-Aguilar, J.F. & Atangana, A. & Owolabi, Kolade M., 2019. "On the dynamics of fractional maps with power-law, exponential decay and Mittag–Leffler memory," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 364-388.
    17. Tassaddiq, Asifa, 2019. "MHD flow of a fractional second grade fluid over an inclined heated plate," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 341-346.
    18. Owolabi, Kolade M. & Atangana, Abdon, 2019. "Computational study of multi-species fractional reaction-diffusion system with ABC operator," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 280-289.
    19. Rayal, Ashish & Ram Verma, Sag, 2020. "Numerical analysis of pantograph differential equation of the stretched type associated with fractal-fractional derivatives via fractional order Legendre wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    20. Hosseininia, M. & Heydari, M.H., 2019. "Legendre wavelets for the numerical solution of nonlinear variable-order time fractional 2D reaction-diffusion equation involving Mittag–Leffler non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 400-407.

    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:136:y:2020:i:c:s0960077920302356. 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.