Higher-order Hahn’s quantum variational calculus

2011/01/19 by Artur M. C. Brito da Cruz, Natália Martins, Natalia Martins +1 · 3 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Applied mathematics #Calculus (dental) #Calculus of variations #Euler's formula #Mathematical Inequalities and Applications #Mathematical analysis #Mathematical functions and polynomials #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Order (exchange) #Physics #Pure mathematics #Quantum #Quantum mechanics #Type (biology) #math.CA #math.OC #msc:39A13 #msc:49K05

paper · pdf · doi:10.1016/j.na.2011.01.015

published as Nonlinear Analysis 75 (2012), no. 3, 1147-1157 · Submitted 30-Sep-2010; revised 4-Jan-2011; accepted 19-Jan-2011; for publication in Nonlinear Analysis Series A: Theory, Methods & Applications

arxiv created 2011/01/19 · openalex publication_date 2011/01/27 · arxiv updated 2011/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We prove a necessary optimality condition of Euler-Lagrange type for quantum variational problems involving Hahn's derivatives of higher-order.

Citations

• Hölderian variational problems subject to integral constraints
• Fractional conservation laws in optimal control theory
• Generalized Euler–Lagrange Equations for Variational Problems with Scale Derivatives
• A fractional calculus of variations for multiple integrals with application to vibrating string
• Necessary optimality conditions for fractional action‐like integrals of variational calculus with Riemann–Liouville derivatives of order (α, β)
• q-Difference Equations

Cited by

• p -variational Calculus
• Fractional Calculus on Time Scales
• Generalizing the variational theory on time scales to include the delta indefinite integral

Related

• Hahn's Symmetric Quantum Variational Calculus
• p -variational Calculus
• Symmetric Quantum Calculus
• Optimality of Finite-Support Parameter Shift Rules for Derivatives of Variational Quantum Circuits
• Noether's Theorem with Momentum and Energy Terms for Cresson's Quantum Variational Problems