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arXiv · 1109.4664

Fractional calculus of variations for 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 ${{^CD}^{\alpha,\beta}_{\gamma}}$, which is a convex combination of the left Caputo fractional derivative of order $\alpha$ and the right Caputo fractional derivative of order $\beta$. The fractional variational problems under our consideration are formulated in terms of ${{^CD}^{\alpha,\beta}_{\gamma}}$. 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. 2011-09-21. Fractional calculus of variations for a combined Caputo derivative. https://doi.org/10.2478/s13540-011-0032-6

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