Hahn's symmetric quantum variational calculus

• Author(s): Brito da Cruz, A. M. C. ; Martins, N. ; Torres, D. F. M.
• Date: 2013
• Persistent ID: http://hdl.handle.net/10773/11874
• Origin: RIA - Repositório Institucional da Universidade de Aveiro
• Subject(s): Calculus of variations; Euler-Lagrange difference equations; Hahn's symmetric calculus; Leitmann's principle; Quantum calculus
• Document Type: Article
• Language: English

Description

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 condi- tion 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.