Journal
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
Volume 147, Issue 3, Pages 419-442Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10957-010-9730-1
Keywords
Hahn's difference operator; Jackson-Norlund's integral; Quantum calculus; Calculus of variations; Leitmann's principle; Ramsey model
Funding
- Portuguese Foundation for Science and Technology (FCT) through the Center for Research and Development in Mathematics and Applications (CIDMA)
- Bialystok University of Technology via Polish Ministry of Science and Higher Education
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We introduce the Hahn quantum variational calculus. Necessary and sufficient optimality conditions for the basic, isoperimetric, and Hahn quantum Lagrange problems, are studied. We also show the validity of Leitmann's direct method for the Hahn quantum variational calculus, and give explicit solutions to some concrete problems. To illustrate the results, we provide several examples and discuss a quantum version of the well known Ramsey model of economics.
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