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The Unique Existence of Weak Solution and the Optimal Control for Time-Fractional Third Grade Fluid System

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  • Guangming Shao
  • Biao Liu
  • Yueying Liu

Abstract

The paper concerns the third grade fluid system with the time-fractional derivative of the order . We first establish unique existence criterion of weak solutions in the case that the dimension . Then we prove the sufficient condition of optimal pairs.

Suggested Citation

  • Guangming Shao & Biao Liu & Yueying Liu, 2018. "The Unique Existence of Weak Solution and the Optimal Control for Time-Fractional Third Grade Fluid System," Complexity, Hindawi, vol. 2018, pages 1-12, November.
    • Handle: RePEc:hin:complx:7941012
    DOI: 10.1155/2018/7941012
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    References listed on IDEAS

    as
    1. Peng, Li & Zhou, Yong & Ahmad, Bashir & Alsaedi, Ahmed, 2017. "The Cauchy problem for fractional Navier–Stokes equations in Sobolev spaces," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 218-228.
    2. Qasem Al-Mdallal & Kashif Ali Abro & Ilyas Khan, 2018. "Analytical Solutions of Fractional Walter’s B Fluid with Applications," Complexity, Hindawi, vol. 2018, pages 1-10, February.
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