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2013, 3(1): 77-94. doi: 10.3934/naco.2013.3.77
Hahn's symmetric quantum variational calculus
Artur M. C. Brito da Cruz 1, , Natália Martins 2, and Delfim F. M. Torres 3,
Escola Superior de Tecnologia de Setúbal, Estefanilha, 2910-761 Setúbal, Portugal
Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
CIDMA — Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
Received December 2011 Revised November 2012 Published January 2013
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.
Keywords: Euler--Lagrange difference equations, quantum calculus., calculus of variations, Leitmann's principle, Hahn's symmetric calculus.
Mathematics Subject Classification: 39A13, 49K0.
Citation: Artur M. C. Brito da Cruz, Natália Martins, Delfim F. M. Torres. Hahn's symmetric quantum variational calculus. Numerical Algebra, Control & Optimization, 2013, 3 (1) : 77-94. doi: 10.3934/naco.2013.3.77
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Artur M. C. Brito da Cruz Natália Martins Delfim F. M. Torres