**5. Discussion**

In this work, we prove the existence and uniqueness of solution for fractional Navier–Stokes equations with variable delays for *α* ∈ ( 1 2 , <sup>1</sup>), and we show that this system is dissipative in the phase space *C H*, namely, there exists a global absorbing set in *C H*. Different from the classic Navier–Stokes equations with variable delays [22–24], in which the existence of pullback absorbing set and pullback attractors were established. Here, we obtained the forward absorbing set, which is more meaningful from the view of applications. Besides, the existence of global attracting set as well as the existence of solution for *α* ∈ (0, 1) in phase space *C H* are still open problems. These will be considered in the future.

**Author Contributions:** Conceptualization, L.F.L. and J.J.N.; methodology, L.F.L. and J.J.N.; writing—original draft preparation, L.F.L.; writing—review and editing, J.J.N. All authors have read and agreed to the published version of the manuscript.

**Funding:** The work of Lin F. Liu has been partially supported by NSF of China (Nos. 11901448, 11871022 and 11671142) as well as by China Postdoctoral Science Foundation Grant (Nos. 2018M643610). The work of Juan J. Nieto has been partially supported by the Agencia Estatal de Investigación (AEI) of Spain, co-financed by the European Fund for Regional Development (FEDER) corresponding to the 2014-2020 multiyear financial framework, project MTM2016-75140-P, Xunta de Galicia under gran<sup>t</sup> ED431C 2019/02; by Instituto de Salud Carlos III (Spain), gran<sup>t</sup> COV20/00617.

**Conflicts of Interest:** The authors declare no conflict of interest.
