Abstract
In this paper, we deal with the problem of controlling the source function for an optimal control problem involving the fractional wave equation. We show that an optimal solution exists and it is unique for the considered fractional optimal control problem. We calculate the Frechet derivative of the cost functional by means of an adjoint problem and derive necessary optimality conditions. Also, we introduce an efficient numerical approximation for the fractional wave equation with the Atangana-Baleanu derivative.
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