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2 2010

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Fractional Euler-Lagrange equations : numerical solutions and applications of reflection operator

100%

Błaszczyk T. , Ciesielski M.

tom Vol. 9, nr 2

17-24

In this work numerical solutions of fractional Euler-Lagrange equations describing free motion are considered. This type of equations contains a composition of left and right fractional derivatives. A reflection operator is applied to obtain relations between the Euler-Lagrange equations. In addition we verify the dependence between the respective numerical schemes using the same operator. In the final part of paper the examples of the numerical solutions are shown.

The delta-nabla calculus of variations

75%

Malinowska A. B. , Torres D. F. M.

2010

tom Nr 44

75-83

The discrete-time, the quantum, and the continuous calculus of variations have been recently unified and extended. Two approaches are followed in the literature: one dealing with minimization of delta integrals; the other dealing with minimization of nabla integrals. Here we propose a more general approach to the calculus of variations on time scales that allows to obtain both delta and nabla results as particular cases.