Hahn's Symmetric Quantum Variational Calculus
Artur M. C. Brito da Cruz, Natalia Martins, Delfim F. M. Torres
TL;DR
This paper develops Hahn's symmetric quantum calculus, deriving optimality conditions for variational problems and demonstrating the effectiveness of Leitmann's direct method with illustrative examples.
Contribution
It introduces Hahn's symmetric quantum calculus and establishes new Euler-Lagrange and sufficiency conditions for variational problems within this framework.
Findings
Derived Euler-Lagrange type necessary conditions.
Established sufficient optimality conditions.
Validated methods with illustrative examples.
Abstract
We introduce and develop the Hahn symmetric quantum calculus with applications to the calculus of variations. Namely, we obtain a necessary optimality condition of Euler-Lagrange type and a sufficient optimality condition for variational problems within the context of Hahn's symmetric calculus. Moreover, we show the effectiveness of Leitmann's direct method when applied to Hahn's symmetric variational calculus. Illustrative examples are provided.
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