271 citations · 1.1k across the 27 of their papers we have counts for
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Existence, uniqueness and controllability for Hilfer differential equations on times scales
J. Vanterler da C. Sousa, D. S. Oliveira, Gastao S. F. Frederico +1
We introduce a new version of -Hilfer fractional derivative, on an arbitrary time scale. The fundamental properties of the new operator are investigated and, in particular, we p…
Noether-type theorem for fractional variational problems depending on fractional derivatives of functions
M. J. Lazo, G. S. F. Frederico, P. M. Carvalho-Neto
In the present work, by taking advantage of a so-called practical limitation of fractional derivatives, namely, the absence of a simple chain and Leibniz's rules, we proposed a gen…
Hight-order Noether's Theorem for Nonsmooth Extremals of Isoperimetric Variational Problems with Time Delay
G. S. F. Frederico, M. J. Lazo
We obtain a nonsmooth higher-order extension of Noether's symmetry theorem for variational isoperimetric problems with delayed arguments. The result is proved to be valid in the cl…
Fractional Noether's Theorem with Classical and Caputo Derivatives: constants of motion for non-conservative systems
Gastão S. F. Frederico, Matheus J. Lazo
Since the seminal work of Emmy Noether it is well know that all conservations laws in physics, \textrm{e.g.}, conservation of energy or conservation of momentum, are directly relat…
Constants of motion for Isoperimetric Variational Problems with Time Delay
G. S. F. Frederico, M. J. Lazo, M. N. F. Barreto +1
In the present work, we obtain the constants of motion for isoperimetric variational problems with time delay. We consider a constrained optimization problem where the Lagrangian f…
Noether's Theorem for Nonsmooth Extremals of Variational Problems with Time Delay
Gastao S. F. Frederico, Tatiana Odzijewicz, Delfim F. M. Torres
We obtain a nonsmooth extension of Noether's symmetry theorem for variational problems with delayed arguments. The result is proved to be valid in the class of Lipschitz functions,…
A Non-Differentiable Quantum Variational Embedding in Presence of Time Delays
Gastao S. F. Frederico, Delfim F. M. Torres
We develop Cresson's non-differentiable embedding to quantum problems of the calculus of variations and optimal control with time delay. Main results show that the dynamics of non-…
Fractional Noether's Theorem with Classical and Riemann-Liouville Derivatives
Gastao S. F. Frederico, Delfim F. M. Torres
We prove a Noether type symmetry theorem to fractional problems of the calculus of variations with classical and Riemann-Liouville derivatives. As result, we obtain constants of mo…
Fractional isoperimetric Noether's theorem in the Riemann-Liouville sense
Gastao S. F. Frederico, Delfim F. M. Torres
We prove Noether-type theorems for fractional isoperimetric variational problems with Riemann-Liouville derivatives. Both Lagrangian and Hamiltonian formulations are obtained. Illu…
Fractional Noether's theorem in the Riesz-Caputo sense
Gastao S. F. Frederico, Delfim F. M. Torres
We prove a Noether's theorem for fractional variational problems with Riesz-Caputo derivatives. Both Lagrangian and Hamiltonian formulations are obtained. Illustrative examples in…
Fractional Optimal Control in the Sense of Caputo and the Fractional Noether's Theorem
Gastao S. F. Frederico, Delfim F. M. Torres
The study of fractional variational problems with derivatives in the sense of Caputo is a recent subject, the main results being Agrawal's necessary optimality conditions of Euler-…
Necessary Optimality Conditions for Fractional Action-Like Problems with Intrinsic and Observer Times
Gastao S. F. Frederico, Delfim F. M. Torres
We prove higher-order Euler-Lagrange and DuBois-Reymond stationary conditions to fractional action-like variational problems. More general fractional action-like optimal control pr…
Non-conservative Noether's theorem for fractional action-like variational problems with intrinsic and observer times
Gastao S. F. Frederico, Delfim F. M. Torres
We extend Noether's symmetry theorem to fractional action-like variational problems with higher-order derivatives.
Fractional conservation laws in optimal control theory
Gastao S. F. Frederico, Delfim F. M. Torres
Using the recent formulation of Noether's theorem for the problems of the calculus of variations with fractional derivatives, the Lagrange multiplier technique, and the fractional…
Conservation laws for invariant functionals containing compositions
Gastao S. F. Frederico, Delfim F. M. Torres
The study of problems of the calculus of variations with compositions is a quite recent subject with origin in dynamical systems governed by chaotic maps. Available results are red…
A Formulation of Noether's Theorem for Fractional Problems of the Calculus of Variations
Gastao S. F. Frederico, Delfim F. M. Torres
Fractional (or non-integer) differentiation is an important concept both from theoretical and applicational points of view. The study of problems of the calculus of variations with…
Constants of motion for fractional action-like variational problems
Gastao S. F. Frederico, Delfim F. M. Torres
We extend Noether's symmetry theorem to the fractional Riemann-Liouville integral functionals of the calculus of variations recently introduced by El-Nabulsi.
Noether's Theorem for Fractional Optimal Control Problems
Gastao S. F. Frederico, Delfim F. M. Torres
We begin by reporting on some recent results of the authors (Frederico and Torres, 2006), concerning the use of the fractional Euler-Lagrange notion to prove a Noether-like theorem…
Nonconservative Noether's Theorem in Optimal Control
Gastao S. F. Frederico, Delfim F. M. Torres
We extend Noether's theorem to dynamical optimal control systems being under the action of nonconservative forces. A systematic way of calculating conservation laws for nonconserva…