Spectral Galerkin Approximation of Fractional Optimal Control Problems with Fractional Laplacian (Advances in Applied Mathematics and Mechanics, 2023)
In this paper spectral Galerkin approximation of optimal control problemgoverned by fractional elliptic equation is investigated. To deal with the nonlocalityof fractional Laplacian operator the Caffarelli-Silvestre extension is utilized. The firstorder optimality condition of the extended optimal control problem is derived. A spectral Galerkin discrete scheme for the extended problem based on weighted Laguerrepolynomials is developed. A priori error estimates for the spectral Galerkin discretescheme is proved. Numerical experiments are presented to show the effectiveness ofour methods and to verify the theoretical findings.