A solution for fractional PDE constrained optimization problems using reduced basis method

Abstract

In this paper, we employ a reduced basis method for solving the PDE constrained optimization problem governed by a fractional parabolic equation with the fractional derivative in time from order β ∈ (0, 1) is defined by Caputo fractional derivative.Here we use optimize-then-discretize method to solve it. In order to this, First, we extract the optimality conditions for the problem, and then solve them by reduced basis method. To get a numerical technique, the time variable is discretized using a finite difference plan. In order to show the effectiveness and accuracy of this method, some test problem are considered, and it is shown that the obtained results are in very good agreement with exact solution.

Solving a category of two‐dimensional fractional optimal control problems using discrete Legendre polynomials

“…A Caputo time‐fractional optimal control problem with inequality constraints is considered by Valian in [16] in which the solution is expanded in terms of Bernoulli wavelet functions. In [17], a method based on reduced basis method and finite difference method is proposed to solve a Caputo fractional optimal control problem.…”