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The Hahn quantum variational calculus. (English) Zbl 1218.49026
Summary: 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.
MSC:
49K10Free problems in several independent variables (optimality conditions)
81Q93Quantum control
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