Optimal control of fractional parabolic systems governing generalized Newtonian fluids

The optimal control problem for the fractional parabolic system governing generalized Newtonian fluids is analyzed in this study. To establish the foundation for the analysis, we employ the variational formulation of the operator system. This approach allows the problem to be expressed in terms of weak solutions. Using the theory of monotone operators, the existence and uniqueness of weak solutions are rigorously demonstrated. Furthermore, the study investigates the optimal control problem associated with the system. The control objective is formulated as a linear quadratic cost functional, which balances the trade-off between achieving desired system behavior and minimizing control effort. The first-order optimality constraints for this problem are derived using the linearized adjoint system.