The Hahn Quantum Variational Calculus
Agnieszka B. Malinowska, Delfim F. M. Torres
TL;DR
This paper introduces the Hahn quantum variational calculus, establishing optimality conditions, validating a direct method, and providing explicit solutions and examples, including an economic model application.
Contribution
It is the first to develop the Hahn quantum variational calculus with comprehensive optimality conditions and solution methods.
Findings
Derived necessary and sufficient optimality conditions.
Validated Leitmann's direct method in the quantum setting.
Provided explicit solutions and applied to an economic model.
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.
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