Necessary Optimality Conditions for Fractional Action-Like Integrals of Variational Calculus with Riemann-Liouville Derivatives of Order $(α,β)$

El-Nabulsi, Rami Ahmad; Torres, Delfim F. M.

Necessary Optimality Conditions for Fractional Action-Like Integrals of Variational Calculus with Riemann-Liouville Derivatives of Order $(α,β)$

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Description

We derive Euler-Lagrange type equations for fractional action-like integrals of the calculus of variations which depend on the Riemann-Liouville derivatives of order $(α,β)$, $α> 0$, $β> 0$, recently introduced by J. Cresson and S. Darses. Some interesting consequences are obtained and discussed.
This is a preprint of an article accepted for publication (28-02-2007) in Math. Methods Appl. Sci