Necessary conditions to a fractional variational problem.

BARRIOS, MELANI; REYERO, GABRIELA; TIDBALL, MABEL

Statistics, Optimization & Information Computing

IAPress

Año: 2022

2311-004X

The fractional variational calculus is a recent field, where classical variational problems are considered, but in the presence of fractional derivatives. Since there are several definitions of fractional derivatives, it is logical to think of different types of optimality conditions. For this reason, in order to solve fractional variational problems, two theorems ofnecessary conditions are well known: an Euler-Lagrange equation which involves Caputo and Riemann-Liouville fractional derivatives, and other Euler-Lagrange equation that involves only Caputo derivatives. However, it is undecided which of these two methods is convenient to work with. In this article, we make a comparison solving a particular fractional variational problem with both methods to obtain some conclusions about which one gives the optimal solution.