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Maple Symbolic Computation in the Calculus of Variations
Andreia M. F. Louro, Delfim F. M. Torres
It is the aim of this work to identify and illustrate the potential and weaknesses of the computer algebra system Maple in the area of the Calculus of Variations: a classical area…
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.
Evolution Strategies in Optimization Problems
Pedro A. F. Cruz, Delfim F. M. Torres
Evolution Strategies are inspired in biology and part of a larger research field known as Evolutionary Algorithms. Those strategies perform a random search in the space of admissib…
Noether's Theorem on Time Scales
Zbigniew Bartosiewicz, Delfim F. M. Torres
We show that for any variational symmetry of the problem of the calculus of variations on time scales there exists a conserved quantity along the respective Euler-Lagrange extremal…