A Simple Accurate Method for Solving Fractional Variational and Optimal Control Problems

TL;DR

This paper introduces a straightforward and precise method for solving fractional variational and optimal control problems by transforming them into classical optimization problems using polynomial fractional derivatives, demonstrating superior accuracy.

Contribution

The paper presents a novel approach that simplifies fractional control problems into static optimization problems, improving accuracy over existing methods.

Findings

The method effectively solves fractional variational problems.

It outperforms recent methods in accuracy.

Examples validate the approach's effectiveness.

Abstract

We develop a simple and accurate method to solve fractional variational and fractional optimal control problems with dependence on Caputo and Riemann-Liouville operators. Using known formulas for computing fractional derivatives of polynomials, we rewrite the fractional functional dynamical optimization problem as a classical static optimization problem. The method for classical optimal control problems is called Ritz's method. Examples show that the proposed approach is more accurate than recent methods available in the literature.