IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v331y2018icp130-139.html
   My bibliography  Save this article

Stokes’ second problem of viscoelastic fluids with constitutive equation of distributed-order derivative

Author

Listed:
  • Duan, Jun-Sheng
  • Qiu, Xiang

Abstract

The steady-state periodic flow of Stokes’ second problem for viscoelastic fluids with constitutive equation in terms of the distributed-order derivative was considered. The distributed-order derivative involves an integration with respect to the order of fractional derivative, and the order is associated with a weight function p(α). With a general weight function p(α), the flow velocity was obtained. The amplitude, the penetration depth and the wavelength were given analytically. Results of Newtonian fluid and single fractional constitutive equation were derived as special cases of weight function p(α). Also we considered other three cases of weight function p(α): linear combination of Dirac delta functions, constant and parameterized exponential function.

Suggested Citation

  • Duan, Jun-Sheng & Qiu, Xiang, 2018. "Stokes’ second problem of viscoelastic fluids with constitutive equation of distributed-order derivative," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 130-139.
    • Handle: RePEc:eee:apmaco:v:331:y:2018:i:c:p:130-139
    DOI: 10.1016/j.amc.2018.02.028
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318301309
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.02.028?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. Fan, Wenping & Jiang, Xiaoyun & Qi, Haitao, 2015. "Parameter estimation for the generalized fractional element network Zener model based on the Bayesian method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 40-49.
    2. Wu, Guo-Cheng & Baleanu, Dumitru & Xie, He-Ping & Chen, Fu-Lai, 2016. "Chaos synchronization of fractional chaotic maps based on the stability condition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 374-383.
    3. Sun, HongGuang & Li, Zhipeng & Zhang, Yong & Chen, Wen, 2017. "Fractional and fractal derivative models for transient anomalous diffusion: Model comparison," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 346-353.
    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. Lei, Dong & Liang, Yingjie & Xiao, Rui, 2018. "A fractional model with parallel fractional Maxwell elements for amorphous thermoplastics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 465-475.
    2. Rujira Ouncharoen & Saowaluck Chasreechai & Thanin Sitthiwirattham, 2020. "Existence and Stability Analysis for Fractional Impulsive Caputo Difference-Sum Equations with Periodic Boundary Condition," Mathematics, MDPI, vol. 8(5), pages 1-17, May.
    3. Darvishi, M.T. & Najafi, Mohammad & Wazwaz, Abdul-Majid, 2021. "Conformable space-time fractional nonlinear (1+1)-dimensional Schrödinger-type models and their traveling wave solutions," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    4. Khennaoui, Amina-Aicha & Ouannas, Adel & Bendoukha, Samir & Grassi, Giuseppe & Lozi, René Pierre & Pham, Viet-Thanh, 2019. "On fractional–order discrete–time systems: Chaos, stabilization and synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 150-162.
    5. Jahanshahi, Hadi & Yousefpour, Amin & Munoz-Pacheco, Jesus M. & Kacar, Sezgin & Pham, Viet-Thanh & Alsaadi, Fawaz E., 2020. "A new fractional-order hyperchaotic memristor oscillator: Dynamic analysis, robust adaptive synchronization, and its application to voice encryption," Applied Mathematics and Computation, Elsevier, vol. 383(C).
    6. Carrera, Y. & Avila-de la Rosa, G. & Vernon-Carter, E.J. & Alvarez-Ramirez, J., 2017. "A fractional-order Maxwell model for non-Newtonian fluids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 276-285.
    7. Du, Feifei & Lu, Jun-Guo, 2021. "New criterion for finite-time synchronization of fractional order memristor-based neural networks with time delay," Applied Mathematics and Computation, Elsevier, vol. 389(C).
    8. Chaudhary, Manish & Kumar, Rohit & Singh, Mritunjay Kumar, 2020. "Fractional convection-dispersion equation with conformable derivative approach," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    9. Gu, Yajuan & Wang, Hu & Yu, Yongguang, 2020. "Synchronization for fractional-order discrete-time neural networks with time delays," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    10. L.J. Basson & Sune Ferreira-Schenk & Zandri Dickason-Koekemoer, 2022. "Fractal Dimension Option Hedging Strategy Implementation During Turbulent Market Conditions in Developing and Developed Countries," International Journal of Economics and Financial Issues, Econjournals, vol. 12(2), pages 84-95, March.
    11. 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.
    12. Prakash, Amit & Kumar, Manoj & Baleanu, Dumitru, 2018. "A new iterative technique for a fractional model of nonlinear Zakharov–Kuznetsov equations via Sumudu transform," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 30-40.
    13. Mo, Lipo & Yuan, Xiaolin & Yu, Yongguang, 2018. "Target-encirclement control of fractional-order multi-agent systems with a leader," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 479-491.
    14. Liu, Xianggang & Ma, Li, 2020. "Chaotic vibration, bifurcation, stabilization and synchronization control for fractional discrete-time systems," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    15. Luo, Cheng & Liu, Bao-Qing & Hou, Hu-Shuang, 2021. "Fractional chaotic maps with q–deformation," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    16. Kirtphaiboon, Sarinya & Humphries, Usa & Khan, Amir & Yusuf, Abdullahi, 2021. "Model of rice blast disease under tropical climate conditions," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    17. Li, Yuxing & Geng, Bo & Jiao, Shangbin, 2022. "Dispersion entropy-based Lempel-Ziv complexity: A new metric for signal analysis," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    18. Weiyuan Ma & Changpin Li & Jingwei Deng, 2019. "Synchronization in Tempered Fractional Complex Networks via Auxiliary System Approach," Complexity, Hindawi, vol. 2019, pages 1-12, November.
    19. Nosrati, Komeil & Shafiee, Masoud, 2018. "Fractional-order singular logistic map: Stability, bifurcation and chaos analysis," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 224-238.
    20. Zhang, Hui & Jiang, Xiaoyun & Yang, Xiu, 2018. "A time-space spectral method for the time-space fractional Fokker–Planck equation and its inverse problem," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 302-318.

    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:apmaco:v:331:y:2018:i:c:p:130-139. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.