An Euler-Lagrange Equation only Depending on Derivatives of Caputo for Fractional Variational Problems with Classical Derivatives

  • Melani Barrios Facultad de Ciencias Exactas, Ingeniería y Agrimensura. Universidad Nacional de Rosario. CONICET
  • Gabriela Reyero Departamento de Matemática- Facultad de Ciencias Exactas, Ingeniería y Agrimensura-Universidad Nacional de Rosario.
Keywords: Fractional Derivatives and Integrals,, Fractional Variational Problems, Euler-Lagrange Fractional Equations

Abstract

In this paper we present advances in fractional variational problems with a Lagrangian depending on Caputofractional and classical derivatives. New formulations of the fractional Euler-Lagrange equation are shown for the basic and isoperimetric problems, one in an integral form, and the other that depends only on the Caputo derivatives. The advantage is that Caputo derivatives are more appropriate for modeling problems than the Riemann-Liouville derivatives and makes the calculations easier to solve because, in some cases, its behavior is similar to the behavior of classical derivatives. Finally, anew exact solution for a particular variational problem is obtained.

Author Biography

Gabriela Reyero, Departamento de Matemática- Facultad de Ciencias Exactas, Ingeniería y Agrimensura-Universidad Nacional de Rosario.
Dra. Gabriela Reyero Profesor Titular -- Departamento de Matemática -- ECENFacultad de Ciencias Exactas, Ingeniería y AgrimensuraUniversidad Nacional de RosarioAv. Pellegrini 250 - 2000 Rosario - Argentina

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Published
2020-05-18
How to Cite
Barrios, M., & Reyero, G. (2020). An Euler-Lagrange Equation only Depending on Derivatives of Caputo for Fractional Variational Problems with Classical Derivatives. Statistics, Optimization & Information Computing, 8(2), 590-601. https://doi.org/10.19139/soic-2310-5070-865
Section
Research Articles