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Spectral Galerkin method for state constrained optimal control of fractional advection‐diffusion‐reaction equations

In this article a spectral Galerkin approximation of fractional advection diffusion optimal control problem with state constraint in L2 norm is discussed. The continuous first order optimality condition is derived. Weighted Jacobi polynomials are used to approximate the state and adjoint state. A priori error estimates for state, adjoint state, and control variables in Hα/2 and weighted L2 norms are derived. Numerical examples are presented to verify the theoretical findings.