Optimal control for obstacle problems involving time-dependent variational inequalities with Liouville–Caputo fractional derivative

Abstract We consider an optimal control problem for a time-dependent obstacle variational inequality involving fractional Liouville–Caputo derivative. The is considered as the control, and corresponding solution to regarded state. Our aim find with properties that state closed given target profile not excessively large in terms of its norm. prove existence results establish necessary conditions problems via approximated time fractional-order partial differential equations their adjoint problems. result this paper generalization parabolic inequalities derivatives were used instead classical derivatives.