@Article{cmc.2020.09897,
AUTHOR = {Abd-Allah Hyder, M. El-Badawy},
TITLE = {Fractional Optimal Control of Navier-Stokes Equations},
JOURNAL = {Computers, Materials \& Continua},
VOLUME = {64},
YEAR = {2020},
NUMBER = {2},
PAGES = {859--870},
URL = {http://www.techscience.com/cmc/v64n2/39333},
ISSN = {1546-2226},
ABSTRACT = {In this paper, the non-stationary incompressible fluid flows governed by the 
Navier-Stokes equations are studied in a bounded domain. This study focuses on the timefractional Navier-Stokes equations in the optimal control subject, where the control is 
distributed within the domain and the time-fractional derivative is proposed as RiemannLiouville sort. In addition, the control object is to minimize the quadratic cost functional. 
By using the Lax-Milgram lemma with the assistance of the fixed-point theorem, we 
demonstrate the existence and uniqueness of the weak solution to this system. Moreover, 
for a quadratic cost functional subject to the time-fractional Navier-Stokes equations, we 
prove the existence and uniqueness of optimal control. Also, via the variational inequality 
upon introducing the adjoint linearized system, some inequalities and identities are given
to guarantee the first-order necessary optimality conditions. A direct consequence of the 
results obtained here is that when α → 1, the obtained results are valid for the classical 
optimal control of systems governed by the Navier-Stokes equations.},
DOI = {10.32604/cmc.2020.09897}
}