TY - JOUR
AU - Melani Barrios
AU - Gabriela Reyero
AU - Mabel Tidball
PY - 2022/02/05
Y2 - 2024/10/13
TI - Necessary Conditions to A Fractional Variational Problem
JF - Statistics, Optimization & Information Computing
JA - Stat., optim. inf. comput.
VL - 10
IS - 2
SE - Research Articles
DO - 10.19139/soic-2310-5070-1047
UR - http://www.iapress.org/index.php/soic/article/view/1047
AB - The fractional variational calculus is a recent fifield, where classical variational problems are considered, but in the presence of fractional derivatives. Since there are several defifinitions 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 of necessary 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.
ER -