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

### 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.### References

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*Statistics, Optimization & Information Computing*,

*8*(2), 590-601. https://doi.org/10.19139/soic-2310-5070-865

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