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arXiv · 1007.0743

Fractional variational calculus in terms of a combined Caputo derivative

Agnieszka B. Malinowska·Delfim F. M. Torres
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Abstract

We generalize the fractional Caputo derivative to the fractional derivative ${^CD^{α,β}_γ}$, which is a convex combination of the left Caputo fractional derivative of order $α$ and the right Caputo fractional derivative of order $β$. The fractional variational problems under our consideration are formulated in terms of ${^CD^{α,β}_γ}$. The Euler-Lagrange equations for the basic and isoperimetric problems, as well as transversality conditions, are proved.

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Agnieszka B. Malinowska, Delfim F. M. Torres. 2010-07-05. Fractional variational calculus in terms of a combined Caputo derivative. https://arxiv.org/abs/1007.0743

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