General quantum variational calculus

  • Artur M. C. Brito da Cruz Escola Superior de Tecnologia de Setubal, Campus do IPS, Estefanilha,Portugal
  • Natalia Martins Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, Portugal
Keywords: General quantum calculus, Hahn's difference operator, Jackson's integral, quantum calculus,


We develop a new variational calculus based in the general quantum difference operator recently introduced by Hamza et al. In particular, we obtain optimality conditions for generalized variational problems where the Lagrangian may depend on the endpoints conditions and a real parameter, for the basic and isoperimetric problems, with and without fixed boundary conditions. Our results provide a generalization to previous results obtained for the $q$- and Hahn-calculus.


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How to Cite
Cruz, A. M. C. B. da, & Martins, N. (2018). General quantum variational calculus. Statistics, Optimization & Information Computing, 6(1), 22-41.
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