Higher-order Hahn's quantum variational calculus
arXiv:1101.3653 · doi:10.1016/j.na.2011.01.015
Abstract
We prove a necessary optimality condition of Euler-Lagrange type for quantum variational problems involving Hahn's derivatives of higher-order.
Submitted 30-Sep-2010; revised 4-Jan-2011; accepted 19-Jan-2011; for publication in Nonlinear Analysis Series A: Theory, Methods & Applications
References in corpus (10)
- Discrete-Time Fractional Variational Problems
- Fractional conservation laws in optimal control theory
- Necessary Optimality Conditions for Fractional Action-Like Integrals of Variational Calculus with Riemann-Liouville Derivatives of Order
- A Fractional Calculus of Variations for Multiple Integrals with Application to Vibrating String
- Calculus of Variations on Time Scales with Nabla Derivatives
- Higher-Order Calculus of Variations on Time Scales
- The Hahn Quantum Variational Calculus
- The isoperimetric problem for Holderian curves
- The diamond-alpha Riemann integral and mean value theorems on time scales
- Generalized Euler-Lagrange equations for variational problems with scale derivatives
Cited by in corpus (14)
- Fractional variational problems depending on indefinite integrals
- Generalized transversality conditions for the Hahn quantum variational calculus
- Generalizing the variational theory on time scales to include the delta indefinite integral
- The power quantum calculus and variational problems
- A symmetric quantum calculus
- Hahn's Symmetric Quantum Variational Calculus
- Higher-order infinite horizon variational problems in discrete quantum calculus
- Fractional Calculus on Time Scales
- The Variational Calculus on Time Scales
- A symmetric Norlund sum with application to inequalities
- Nondifferentiable variational principles in terms of a quantum operator
- Noether's Theorem with Momentum and Energy Terms for Cresson's Quantum Variational Problems
- A -Sturm Liouville problem associated with the general quantum operator
- Helmholtz theorem for nondifferentiable Hamiltonian systems in the framework of Cresson's quantum calculus