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

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

2007-02-28

arxiv.org/abs/math-ph/0702099v1

Math. Methods Appl. Sci. (2007), Vol. 30, Issue 15, pp. 1931--1939

Physics

Mathematical Physics

This is a preprint of an article accepted for publication (28-02-2007) in Math. Methods Appl. Sci

Scientific paper

10.1002/mma.879

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 $(\alpha,\beta)$, $\alpha > 0$, $\beta > 0$, recently introduced by J.
Cresson and S. Darses. Some interesting consequences are obtained and
discussed.

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