Fractional Calculus of Variations: a novel way to look at it

TL;DR

This paper presents a new perspective on fractional calculus of variations, demonstrating that a fractional generalization of classical problems can have solutions without restrictions on the derivative order.

Contribution

It introduces a novel approach to fractional calculus of variations, removing previous limitations on the derivative order for solutions.

Findings

Fractional calculus of variations can be approached differently.

Solutions exist without restrictions on the fractional derivative order.

The method simplifies the analysis of fractional variational problems.

Abstract

In this work we look at the original fractional calculus of variations problem in a somewhat different way. As a simple consequence, we show that a fractional generalization of a classical problem has a solution without any restrictions on the derivative-order $\alpha$.