The Legendre pseudospectral method for a time-fractionaloptimal control problem

In this article a numerical scheme based on the Legendrepseudo spectral and finitediffference methods is presented to solve an optimal control problem (OCP) governedby a fractional diffusion equation. Using the pseudospectral derivative matrices, thisOCP reduces to a nonlinear optimization problem (NOP). Moreover, it is shown thatthe Karush-Kuhn-Tucker conditions of the derived NOP are exactly equivalent to thediscretized form of its Ponteryagin optimal conditions. To demonstrate the efficiencyof the proposed method, some numerical results are provided.