Fractional calculus of variations for a combined Caputo derivative

Details Fractional calculus of variations for a combined Caputo derivative Fractional calculus of variations for a combined Caputo derivative

2011-09-21

arxiv.org/abs/1109.4664v1

Fract. Calc. Appl. Anal., Vol. 14, No 4 (2011), pp. 523--537

Mathematics

Optimization and Control

This is a preprint of a paper whose final and definite form has been published in: Fract. Calc. Appl. Anal., Vol. 14, No 4 (20

Scientific paper

10.2478/s13540-011-0032-6

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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