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The Hahn Quantum Variational Calculus

Author

Listed:
  • A. B. Malinowska

    (Białystok University of Technology)

  • D. F. M. Torres

    (University of Aveiro)

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.

Suggested Citation

  • A. B. Malinowska & D. F. M. Torres, 2010. "The Hahn Quantum Variational Calculus," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 419-442, December.
    • Handle: RePEc:spr:joptap:v:147:y:2010:i:3:d:10.1007_s10957-010-9730-1
    DOI: 10.1007/s10957-010-9730-1
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    References listed on IDEAS

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    1. D. A. Carlson & G. Leitmann, 2005. "Coordinate Transformation Method for the Extremization of Multiple Integrals," Journal of Optimization Theory and Applications, Springer, vol. 127(3), pages 523-533, December.
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    10. Dean A. Carlson & George Leitmann, 2005. "A Direct Method for Open-Loop Dynamic Games for Affine Control Systems," Springer Books, in: Alain Haurie & Georges Zaccour (ed.), Dynamic Games: Theory and Applications, chapter 0, pages 37-55, Springer.
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    Cited by:

    1. M. H. Annaby & A. E. Hamza & K. A. Aldwoah, 2012. "Hahn Difference Operator and Associated Jackson–Nörlund Integrals," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 133-153, July.
    2. Nichaphat Patanarapeelert & Thanin Sitthiwirattham, 2019. "On Fractional Symmetric Hahn Calculus," Mathematics, MDPI, vol. 7(10), pages 1-18, September.

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