A Discretization Method to Solve Fractional Variational Problems with Dependence on Hadamard Derivatives

TL;DR

This paper introduces a quick and straightforward discretization approach to solve fractional variational problems involving Hadamard derivatives by converting them into classical optimal control problems and applying standard numerical methods.

Contribution

The paper presents a novel discretization method that transforms fractional variational problems with Hadamard derivatives into classical control problems for easier numerical solution.

Findings

Effective conversion of fractional problems to classical control problems

Simplified numerical solution process demonstrated with an example

Potential for faster solutions to fractional variational problems

Abstract

We provide a fast and simple method to solve fractional variational problems with dependence on Hadamard fractional derivatives. Using a relation between the Hadamard fractional operator and a sum involving integer-order derivatives, we rewrite the fractional problem into a classical optimal control problem. The latter problem is then solved by application of standard numerical techniques. We illustrate the procedure with an example.