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

TL;DR

This paper introduces a reduced basis method tailored for efficiently solving PDE-constrained optimization problems involving fractional parabolic equations with Caputo derivatives, enabling faster computations.

Contribution

The paper develops a novel reduced basis approach specifically designed for fractional PDE constrained optimization problems, addressing computational challenges.

Findings

Effective reduction in computational complexity.

Accurate solutions demonstrated on fractional PDE problems.

Potential for real-time optimization applications.

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 beta in (0,1) is defined by Caputo fractional derivative.