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We adopt the integral definition of the fractional Laplace operator andanalyze solution techniques for fractional, semilinear, and elliptic optimalcontrol problems posed on Lipschitz polytopes. We consider two strategies ofdiscretization: a semidiscrete scheme where the admissible control set is notdiscretized and a fully discrete scheme where such a set is discretized withpiecewise constant functions. As an instrumental step, we derive errorestimates for finite element discretizations of fractional semilinear ellipticpartial differential equations (PDEs) on quasi-uniform and graded meshes. Withthese estimates at hand, we derive error bounds for the semidiscrete scheme andimprove the ones that are available in the literature for the fully discretescheme.

Error estimates for fractional semilinear optimal control on Lipschitz polytopes