Fractional Noether's theorem in the Riesz-Caputo sense
arXiv:1001.4507 · doi:10.1016/j.amc.2010.01.100
Abstract
We prove a Noether's theorem for fractional variational problems with Riesz-Caputo derivatives. Both Lagrangian and Hamiltonian formulations are obtained. Illustrative examples in the fractional context of the calculus of variations and optimal control are given.
Accepted (25/Jan/2010) for publication in Applied Mathematics and Computation
References in corpus (17)
- A Formulation of Noether's Theorem for Fractional Problems of the Calculus of Variations
- Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives
- 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
- Necessary Optimality Conditions for Fractional Action-Like Integrals of Variational Calculus with Riemann-Liouville Derivatives of Order
- Fractional embedding of differential operators and Lagrangian systems
- A Fractional Calculus of Variations for Multiple Integrals with Application to Vibrating String
- Leitmann's direct method for fractional optimization problems
- Leitmann's direct method of optimization for absolute extrema of certain problems of the calculus of variations on time scales
- Constants of motion for fractional action-like variational problems
- Quasi-Invariant Optimal Control Problems
- Automatic Computation of Conservation Laws in the Calculus of Variations and Optimal Control
- Symbolic Computation of Variational Symmetries in Optimal Control
- Contrasting Two Transformation-Based Methods for Obtaining Absolute Extrema
- Conservation laws for invariant functionals containing compositions
- Non-conservative Noether's theorem for fractional action-like variational problems with intrinsic and observer times
Cited by in corpus (34)
- A New Approach to Generalized Fractional Derivatives
- Discrete-Time Fractional Variational Problems
- Fractional Variational Calculus with Classical and Combined Caputo Derivatives
- The generalized natural boundary conditions for fractional variational problems in terms of the Caputo derivative
- Variational Calculus with Conformable Fractional Derivatives
- Fractional calculus of variations for a combined Caputo derivative
- Generalized fractional calculus with applications to the calculus of variations
- A formulation of the fractional Noether-type theorem for multidimensional Lagrangians
- Fractional variational problems depending on indefinite integrals
- Discrete Direct Methods in the Fractional Calculus of Variations
- Fractional variational calculus of variable order
- Fractional variational calculus for nondifferentiable functions
- Leitmann's direct method for fractional optimization problems
- Fractional Dynamics of Network Growth Constrained by aging Node Interactions
- Fractional Calculus for Continuum Mechanics - anisotropic non-locality
- Noether's Symmetry Theorem for Variational and Optimal Control Problems with Time Delay
- Variational problems of Herglotz type with time delay: DuBois-Reymond condition and Noether's first theorem
- Multiobjective fractional variational calculus in terms of a combined Caputo derivative
- Non-local fractional model of rate independent plasticity
- Fractional Euler-Lagrange differential equations via Caputo derivatives
- Towards a combined fractional mechanics and quantization
- Noether's Theorem for Nonsmooth Extremals of Variational Problems with Time Delay
- Composition Functionals in Fractional Calculus of Variations
- Noether's theorem for fractional variational problems of variable order
- Fractional isoperimetric Noether's theorem in the Riemann-Liouville sense
- Isoperimetric problems of the calculus of variations with fractional derivatives
- Fractional Calculus on Time Scales
- Fractional Calculus of Variations of Several Independent Variables
- Fractional variational calculus in terms of a combined Caputo derivative
- Fractional Noether's Theorem with Classical and Riemann-Liouville Derivatives
- A class of fractional optimal control problems and fractional Pontryagin's systems. Existence of a fractional Noether's theorem
- Fractional Calculus of Variations for Double Integrals
- Variational Problems Involving a Caputo-Type Fractional Derivative
- A Necessary Optimality Condition for Extended Weighted Generalized Fractional Optimal Control Problems