The Hahn Quantum Variational Calculus

A. B. Malinowska () and D. F. M. Torres ()
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A. B. Malinowska: Białystok University of Technology
D. F. M. Torres: University of Aveiro

Journal of Optimization Theory and Applications, 2010, vol. 147, issue 3, No 1, 419-442

Abstract: Abstract 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.

Keywords: Hahn’s difference operator; Jackson–Norlünd’s integral; Quantum calculus; Calculus of variations; Leitmann’s principle; Ramsey model (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-010-9730-1

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