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

Abstract

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.

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

References in corpus (3)

• A Formulation of Noether's Theorem for Fractional Problems of the Calculus of Variations
• Fractional embedding of differential operators and Lagrangian systems
• Constants of motion for fractional action-like variational problems

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