# Necessary Conditions to A Fractional Variational Problem

• Melani Barrios Facultad de Ciencias Exactas, Ingeniería y Agrimensura. Universidad Nacional de Rosario. CONICET, Argentina
• Gabriela Reyero Departamento de Matem´atica, Facultad de Ciencias Exactas, Ingenier´ıa y Agrimensura, Universidad Nacional de Rosario, Argentina
• Mabel Tidball CEE-M, Univ. Montpellier, CNRS, INRAE, Institut Agro, Montpellier, France
Keywords: Fractional Derivatives and Integrals, Fractional Variational Problems, Euler-Lagrange Fractional Equations, Caputo Derivatives, Riemann-Liouville Derivatives

### Abstract

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.

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Published
2022-02-05
How to Cite
Barrios, M., Reyero, G., & Tidball, M. (2022). Necessary Conditions to A Fractional Variational Problem. Statistics, Optimization & Information Computing, 10(2), 426-438. https://doi.org/10.19139/soic-2310-5070-1047
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Research Articles