Fractional variational calculus in terms of a combined Caputo derivative

Details Fractional variational calculus in terms of a combined Caputo derivative Fractional variational calculus in terms of a combined Caputo derivative

2010-07-05

arxiv.org/abs/1007.0743v1

Proc. 4th IFAC Workshop Fract. Differ. Appl. (2010), art. no. FDA10-084, 6pp

Mathematics

Optimization and Control

Submitted 30-April-2010; accepted 23-June-2010; for presentation at the IFAC Workshop on Fractional Derivative and Application

Scientific paper

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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