Artur M. C. Brito da Cruz, Natalia Martins, Delfim F. M. Torres
Published 2012-09-07Version 1
We introduce and develop the Hahn symmetric quantum calculus with applications to the calculus of variations. Namely, we obtain a necessary optimality condition of Euler-Lagrange type and a sufficient optimality condition for variational problems within the context of Hahn's symmetric calculus. Moreover, we show the effectiveness of Leitmann's direct method when applied to Hahn's symmetric variational calculus. Illustrative examples are provided.
Comments: This is a preprint of a paper whose final and definite form will appear in the international journal Numerical Algebra, Control and Optimization (NACO). Paper accepted for publication 06-Sept-2012
Journal: Numer. Algebra Control Optim. 3 (2013), no. 1, 77--94
Higher-order Hahn's quantum variational calculus
Leitmann's direct method of optimization for absolute extrema of certain problems of the calculus of variations on time scales
Existence of minimizers for generalized Lagrangian functionals and a necessary optimality condition --- Application to fractional variational problems
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