IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v130y2020ics096007791930400x.html
   My bibliography  Save this article

Hydromagnetic flow over a moving plate of second grade fluids with time fractional derivatives having non-singular kernel

Author

Listed:
  • Fetecau, C.
  • Zafar, A.A.
  • Vieru, D.
  • Awrejcewicz, J.

Abstract

Hydromagnetic flow of second grade fluids with time fractional derivatives without singular kernel over an infinite moving plate is analytically studied. Two equivalent general solutions are established for non-dimensional velocity field using Laplace and Fourier sine transforms. They can be utilized to produce exact solutions of the problems involving any motion of this kind of these fluids. For validation and highlighting the impact of fractional parameter upon the fluid dynamics, the solutions of the Stokes’ problems are brought to light. They are presented as sums of transient and permanent solutions. Moreover, the time consumed in convergence to the equilibrium-state is presented graphically. A comparison between models is also included in the case of the first Stokes’ problem. The flow of fractional order fluids has been found faster as compared to the ordinary fluids at smaller time steps. After a short time the ordinary fluids flow faster and the non-Newtonian effects and the impact of non-integer parameter upon the fluid velocity vanish in time. The present work also witnesses that the time consumed in attaining the equilibrium state for the sine oscillations based plate motions is greater than those of induced by cosine oscillations based plate motions.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:130:y:2020:i:c:s096007791930400x
    DOI: 10.1016/j.chaos.2019.109454
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007791930400X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2019.109454?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. 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.
    2. 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.
    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)

    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. 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.
    2. 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).
    3. 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.
    4. 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).
    5. 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).
    6. 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).
    7. 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).
    8. Uçar, Sümeyra & Uçar, Esmehan & Özdemir, Necati & Hammouch, Zakia, 2019. "Mathematical analysis and numerical simulation for a smoking model with Atangana–Baleanu derivative," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 300-306.
    9. Zafar, Zain Ul Abadin & Zaib, Sumera & Hussain, Muhammad Tanveer & Tunç, Cemil & Javeed, Shumaila, 2022. "Analysis and numerical simulation of tuberculosis model using different fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    10. 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.
    11. 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.
    12. Prakash, Amit & Kaur, Hardish, 2019. "Analysis and numerical simulation of fractional order Cahn–Allen model with Atangana–Baleanu derivative," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 134-142.
    13. 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.
    14. 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).
    15. Ali, Farhad & Ali, Farman & Sheikh, Nadeem Ahmad & Khan, Ilyas & Nisar, Kottakkaran Sooppy, 2020. "Caputo–Fabrizio fractional derivatives modeling of transient MHD Brinkman nanoliquid: Applications in food technology," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    16. Taneco-Hernández, M.A. & Morales-Delgado, V.F. & Gómez-Aguilar, J.F., 2019. "Fundamental solutions of the fractional Fresnel equation in the real half-line," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 807-827.
    17. 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.
    18. 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.
    19. Sun, HongGuang & Hao, Xiaoxiao & Zhang, Yong & Baleanu, Dumitru, 2017. "Relaxation and diffusion models with non-singular kernels," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 590-596.
    20. Odibat, Zaid & Baleanu, Dumitru, 2023. "A new fractional derivative operator with generalized cardinal sine kernel: Numerical simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 224-233.

    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:130:y:2020:i:c:s096007791930400x. 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.