Hahn's Symmetric Quantum Variational Calculus

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.

This is a preprint of a paper whose final and definite form will appear in the international journal Numerical Algebra, Control and Optimization (NACO). Paper accepted for publication 06-Sept-2012

References in corpus (9)

• Information in Black Hole Radiation
• The Hahn Quantum Variational Calculus
• q-Deformed Conformal Quantum Mechanics
• Leitmann's direct method for fractional optimization problems
• Leitmann's direct method of optimization for absolute extrema of certain problems of the calculus of variations on time scales
• Higher-order Hahn's quantum variational calculus
• The power quantum calculus and variational problems
• Higher-order infinite horizon variational problems in discrete quantum calculus
• Contrasting Two Transformation-Based Methods for Obtaining Absolute Extrema

Cited by in corpus (5)

• A Fractional Calculus on Arbitrary Time Scales: Fractional Differentiation and Fractional Integration
• The Diamond Integral on Time Scales
• Nonsymmetric and Symmetric Fractional Calculi on Arbitrary Nonempty Closed Sets
• Noether's Theorem with Momentum and Energy Terms for Cresson's Quantum Variational Problems
• Helmholtz theorem for nondifferentiable Hamiltonian systems in the framework of Cresson's quantum calculus