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 (1)

• A Formulation of Noether's Theorem for Fractional Problems of the Calculus of Variations

Cited by in corpus (3)

• Fractional conservation laws in optimal control theory
• Fractional Action-Like Variational Problems
• Fractional Optimal Control in the Sense of Caputo and the Fractional Noether's Theorem