General quantum variational calculus

Artur M. C. Brito da Cruz, Natalia Martins

Abstract


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.

Keywords


General quantum calculus; Hahn's difference operator; Jackson's integral; quantum calculus;

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DOI: 10.19139/soic.v6i1.467

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