The Legendre pseudospectral method for a time-fractional optimal‎ ‎control problem

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