The Hahn Quantum Variational Calculus
arXiv:1006.3765 · doi:10.1007/s10957-010-9730-1
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.
Submitted: 3/March/2010; 4th revision: 9/June/2010; accepted: 18/June/2010; for publication in Journal of Optimization Theory and Applications
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Cited by in corpus (12)
- Generalized transversality conditions for the Hahn quantum variational calculus
- Higher-order Hahn's quantum variational calculus
- Fractional Euler-Lagrange differential equations via Caputo derivatives
- Generalizing the variational theory on time scales to include the delta indefinite integral
- Existence of solutions for dynamic inclusions on time scales via duality
- A symmetric quantum calculus
- Hahn's Symmetric Quantum Variational Calculus
- Higher-order infinite horizon variational problems in discrete quantum calculus
- The Variational Calculus on Time Scales
- A symmetric Norlund sum with application to inequalities
- Nondifferentiable variational principles in terms of a quantum operator
- Helmholtz theorem for nondifferentiable Hamiltonian systems in the framework of Cresson's quantum calculus