@Article{AAMM-15-6,
author = {Zhang, Jiaqi and Yin, Yang and Zhou, Zhaojie},
title = {Spectral Galerkin Approximation of Fractional Optimal Control Problems with Fractional Laplacian},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2023},
volume = {15},
number = {6},
pages = {1631--1654},
abstract = {<p style="text-align: justify;">In this paper spectral Galerkin approximation of optimal control problem
governed by fractional elliptic equation is investigated. To deal with the nonlocality
of fractional Laplacian operator the Caffarelli-Silvestre extension is utilized. The first
order optimality condition of the extended optimal control problem is derived. A spectral Galerkin discrete scheme for the extended problem based on weighted Laguerre
polynomials is developed. A priori error estimates for the spectral Galerkin discrete
scheme is proved. Numerical experiments are presented to show the effectiveness of
our methods and to verify the theoretical findings.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2022-0173},
url = {https://global-sci.com/article/72886/spectral-galerkin-approximation-of-fractional-optimal-control-problems-with-fractional-laplacian}
}