Necessary conditions to a fractional variational problem

TL;DR

This paper compares two necessary condition methods for fractional variational problems involving Caputo and Riemann-Liouville derivatives to determine which yields the optimal solution.

Contribution

It provides a comparative analysis of two Euler-Lagrange equations involving different fractional derivatives for solving variational problems.

Findings

The method involving both Caputo and Riemann-Liouville derivatives can be contrasted to identify optimal solutions.

The paper offers insights into the effectiveness of each method for specific fractional variational problems.

Abstract

In order to solve fractional variational problems, there exist two theorems of necessary conditions: an Euler-Lagrange equation which involves Caputo and Riemann-Liouville fractional derivatives, and other Euler-Lagrange equation that involves only Caputo derivatives. In this article, we make a comparison solving a particular fractional variational problem with both methods to obtain some conclusions about which method gives the optimal solution.