A formulation of the fractional Noether-type theorem for multidimensional Lagrangians

Abstract

This paper presents the Euler-Lagrange equations for fractional variational problems with multiple integrals. The fractional Noether-type theorem for conservative and nonconservative generalized physical systems is proved. Our approach uses well-known notion of the Riemann-Liouville fractional derivative.

Submitted 26-SEP-2011; accepted 3-MAR-2012; for publication in Applied Mathematics Letters

References in corpus (12)

• A Formulation of Noether's Theorem for Fractional Problems of the Calculus of Variations
• Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives
• Fractional Action-Like Variational Problems
• Fractional Optimal Control in the Sense of Caputo and the Fractional Noether's Theorem
• Fractional Noether's theorem in the Riesz-Caputo sense
• Necessary Optimality Conditions for Fractional Action-Like Integrals of Variational Calculus with Riemann-Liouville Derivatives of Order $(\alpha ,\beta )$
• Fractional embedding of differential operators and Lagrangian systems
• Fractional Variational Calculus with Classical and Combined Caputo Derivatives
• A Fractional Calculus of Variations for Multiple Integrals with Application to Vibrating String
• Hamiltonian formalism of fractional systems
• Multiobjective fractional variational calculus in terms of a combined Caputo derivative
• Composition Functionals in Fractional Calculus of Variations

Cited by in corpus (3)

• Fractional Calculus of Variations of Several Independent Variables
• The second Noether theorem on time scale
• Conservation laws for time-fractional subdiffusion and diffusion-wave equations