Fractional Action-Like Variational Problems

Abstract

Fractional action-like variational problems have recently gained importance in studying dynamics of nonconservative systems. In this note we address multi-dimensional fractional action-like problems of the calculus of variations.

This is a preprint of an article accepted for publication (28-04-2008) in J. Math. Phys

References in corpus (10)

• A Formulation of Noether's Theorem for Fractional Problems of the Calculus of Variations
• Fractional conservation laws in optimal control theory
• 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 Generalization of Gradient and Hamiltonian Systems
• Fractional Variations for Dynamical Systems: Hamilton and Lagrange Approaches
• Constants of motion for fractional action-like variational problems
• Periodical Solutions of Multi-Time Hamilton Equations
• Non-conservative Noether's theorem for fractional action-like variational problems with intrinsic and observer times
• Necessary Optimality Conditions for Fractional Action-Like Problems with Intrinsic and Observer Times

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