Helmholtz theorem for nondifferentiable Hamiltonian systems in the framework of Cresson's quantum calculus

Abstract

We derive the Helmholtz theorem for nondifferentiable Hamiltonian systems in the framework of Cresson's quantum calculus. Precisely, we give a theorem characterizing nondifferentiable equations, admitting a Hamiltonian formulation. Moreover, in the affirmative case, we give the associated Hamiltonian.

This is a preprint of a paper whose final and definite form is in 'Discrete Dynamics in Nature and Society', ISSN: 1026-0226 (Print), ISSN: 1607-887X (Online), available at [http://dx.doi.org/10.1155/2016/8073023]. Submitted 23-Jan-2016; Revised 21-Feb-2016; Accepted 28-April-2016. Minor corrections, detected during the reading of the proofs, were done in this third version of the preprint. arXiv admin note: text overlap with arXiv:1405.2996

References in corpus (13)

• The Hahn Quantum Variational Calculus
• The isoperimetric problem for Holderian curves
• Generalized transversality conditions for the Hahn quantum variational calculus
• A symmetric quantum calculus
• Hahn's Symmetric Quantum Variational Calculus
• Higher-order infinite horizon variational problems in discrete quantum calculus
• Generalized Euler-Lagrange equations for variational problems with scale derivatives
• A Non-Differentiable Quantum Variational Embedding in Presence of Time Delays
• A symmetric Norlund sum with application to inequalities
• Necessary condition for an Euler-Lagrange equation on time scales
• Helmholtz theorem for stochastic Hamiltonian systems
• Noether's Theorem with Momentum and Energy Terms for Cresson's Quantum Variational Problems
• L'Hopital-Type Rules for Monotonicity with Application to Quantum Calculus