A symmetric quantum calculus

Abstract

We introduce the $\alpha ,\beta$-symmetric difference derivative and the $\alpha ,\beta$-symmetric Nörlund sum. The associated symmetric quantum calculus is developed, which can be seen as a generalization of the forward and backward $h$-calculus.

Submitted 26/Sept/2011; accepted in revised form 28/Dec/2011; to Proceedings of International Conference on Differential & Difference Equations and Applications, in honour of Professor Ravi P. Agarwal, to be published by Springer in the series Proceedings in Mathematics (PROM)

References in corpus (2)

• The Hahn Quantum Variational Calculus
• The diamond-alpha Riemann integral and mean value theorems on time scales

Cited by in corpus (3)

• 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