Fractional Noether's theorem in the Riesz-Caputo sense
From MaRDI portal
Publication:603059
DOI10.1016/j.amc.2010.01.100zbMath1200.49019arXiv1001.4507OpenAlexW1963577778WikidataQ57651111 ScholiaQ57651111MaRDI QIDQ603059
Delfim F. M. Torres, Gastão S. F. Frederico
Publication date: 5 November 2010
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1001.4507
optimal controlinvariancefractional derivativescalculus of variationsNoether's theoremLeitmann's direct method
Optimality conditions for problems involving ordinary differential equations (49K15) Fractional ordinary differential equations (34A08)
Related Items
Variational problem of Herglotz type for Birkhoffian system and its Noether's theorems, Analysis of elastic-viscoplastic creep model based on variable-order differential operator, Existence of optimal solutions to Lagrange problem for a fractional nonlinear control system with Riemann-Liouville derivative, On the existence of optimal solutions to fractional optimal control problems, Lattice fractional diffusion equation in terms of a Riesz-Caputo difference, Composition functionals in higher order calculus of variations and Noether's theorem, Weighted hypergeometric functions and fractional derivative, Noether symmetries and conserved quantities for fractional forced Birkhoffian systems, Plane strain and plane stress elasticity under fractional continuum mechanics, Conserved quantities and adiabatic invariants for El-Nabulsi's fractional Birkhoff system, Discrete direct methods in the fractional calculus of variations, Noether symmetries and conserved quantities for fractional Birkhoffian systems, Legendre spectral collocation method for distributed and Riesz fractional convection-diffusion and Schrödinger-type equation, Fractional Noether's theorem with classical and Caputo derivatives: constants of motion for non-conservative systems, Generalized fractional calculus with applications to the calculus of variations, Fractional isoperimetric Noether's theorem in the Riemann-Liouville sense, Leitmann's direct method for fractional optimization problems, About the Noether's theorem for fractional Lagrangian systems and a generalization of the classical Jost method of proof, Euler-Lagrange equations for Lagrangians containing complex-order fractional derivatives, Calculus of variations with hyperdifferential operators from Tabasaki-Takebe-Toda lattice arguments, Fractional integro-differential calculus and its control-theoretical applications. I: Mathematical fundamentals and the problem of interpretation, Discrete-time fractional variational problems, An extended formulation of calculus of variations for incommensurate fractional derivatives with fractional performance index, Local and global conserved quantities involving generalized operators, On solvability of differential equations with the Riesz fractional derivative, Information space of multi-sensor networks, Lie symmetries and their inverse problems of nonholonomic Hamilton systems with fractional derivatives, Noether symmetries for fractional generalized Birkhoffian systems in terms of classical and combined Caputo derivatives, Generalization of Noether theorem and action principle for non-Lagrangian theories, The fractional white dwarf hydrodynamical nonlinear differential equation and emergence of quark stars, Dissipativity and stability for a nonlinear differential equation with distributed order symmetrized fractional derivative, Multiobjective fractional variational calculus in terms of a combined Caputo derivative, General fractional classical mechanics: action principle, Euler-Lagrange equations and Noether theorem, Noether's theorem for fractional variational problem from El-Nabulsi extended exponentially fractional integral in phase space, Symmetries and conserved quantities for fractional action-like Pfaffian variational problems, Fractional variational calculus for nondifferentiable functions, Generalized multiparameters fractional variational calculus, Generalized Euler-Lagrange equations for fractional variational problems with free boundary conditions, Fractional variational problems depending on indefinite integrals, Fractional variational calculus with classical and combined Caputo derivatives, Generalized variational calculus in terms of multi-parameters fractional derivatives, Application of fractional continuum mechanics to rate independent plasticity, Fractional variational problems with the Riesz-Caputo derivative, Generalized fractional isoperimetric problem of several variables, A theoretical analysis of the free axial vibration of non-local rods with fractional continuum mechanics, Lie symmetries and conserved quantities of the constraint mechanical systems on time scales, Noether's theorem of fractional Birkhoffian systems, Fractional Variational Calculus of Variable Order, Noether’s theorem for non-smooth extremals of variational problems with time delay, Fractional variational problems from extended exponentially fractional integral, Direct solution of a type of constrained fractional variational problems via an adaptive pseudospectral method, A formulation of the fractional Noether-type theorem for multidimensional Lagrangians, Generalized natural boundary conditions for fractional variational problems in terms of the Caputo derivative, Fractional linear control systems with Caputo derivative and their optimization, A new approach on fractional variational problems and Euler-Lagrange equations, Noether symmetry and conserved quantity for fractional Birkhoffian mechanics and its applications, Legendre's necessary condition for fractional Bolza functionals with mixed initial/final constraints, On fractional variational problems which admit local transformations, Optimal control of non-smooth fractional-order systems based on extended Caputo derivative, Towards a combined fractional mechanics and quantization, Fractional calculus of variations for a combined Caputo derivative, Unnamed Item, Caputo \(\Delta\)-type fractional time-scales Noether theorem of Birkhoffian systems, A counterexample to a Frederico-Torres fractional Noether-type theorem, Spectral solutions for a class of nonlinear wave equations with Riesz fractional based on Legendre collocation technique, Pontryagin maximum principle for fractional ordinary optimal control problems, Variational problems of Herglotz type with time delay: DuBois-Reymond condition and Noether's first theorem
Cites Work
- 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
- Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives
- Fractional conservation laws in optimal control theory
- Contrasting two transformation-based methods for obtaining absolute extrema
- A formulation of Noether's theorem for fractional problems of the calculus of variations
- Explicit solutions of fractional integral and differential equations involving Erdélyi-Kober operators
- Integrals involving complete elliptic integrals
- Quasi-invariant optimal control problems
- Proper extensions of Noether's symmetry theorem for nonsmooth extremals of the calculus of variations
- An extension of the coordinate transformation method for open-loop Nash equilibria
- Hamiltonian formulation of systems with linear velocities within Riemann-Liouville fractional derivatives
- Coordinate transformation method for the extremization of multiple integrals
- On the Noether theorem for optimal control
- A note on absolute extrema of certain integrals
- Fractional embedding of differential operators and Lagrangian systems
- Generalized Euler—Lagrange Equations and Transversality Conditions for FVPs in terms of the Caputo Derivative
- Fractional Optimal Control in the Sense of Caputo and the Fractional Noether's Theorem
- COMPLEXIFIED FRACTIONAL HEAT KERNEL AND PHYSICS BEYOND THE SPECTRAL TRIPLET ACTION IN NONCOMMUTATIVE GEOMETRY
- On the Efficacy of Nonlinear Control in Uncertain Linear Systems
- Composition of erdélyi-kober fractional operators
- Noether's theorem for optimum control systems
- A fractional calculus of variations for multiple integrals with application to vibrating string
- Fractional variational calculus in terms of Riesz fractional derivatives
- AN EXTENSION OF LEITMANN'S DIRECT METHOD TO INEQUALITY CONSTRAINTS
- Computação Algébrica no Cálculo das Variações: Determinação de Simetrias e Leis de Conservação
- Necessary optimality conditions for fractional action‐like integrals of variational calculus with Riemann–Liouville derivatives of order (α, β)
- Conservation laws for invariant functionals containing compositions§
- Fractional actionlike variational problems
- On a class of direct optimization problems
- Some extensions to a direct optimization method
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item