Symmetric Quantum Calculus
Abstract
We generalize the Hahn variational calculus by studying problems of the calculus of variations with higher-order derivatives. The symmetric quantum calculus is studied, namely the -symmetric, the -symmetric, and the Hahn symmetric quantum calculus. We introduce the symmetric quantum variational calculus and an Euler-Lagrange type equation for the -symmetric and Hahn's symmetric quantum calculus is proved. We define a symmetric derivative on time scales and derive some of its properties. Finally, we introduce and study the diamond integral, which is a refined version of the diamond- integral on time scales.
Keywords
Cite
@article{arxiv.1306.1327,
title = {Symmetric Quantum Calculus},
author = {Artur M. C. Brito da Cruz},
journal= {arXiv preprint arXiv:1306.1327},
year = {2013}
}
Comments
PhD thesis, Doctoral Programme in Mathematics and Applications (PDMA), University of Aveiro and University of Minho, 2012. Supervisor: Delfim F. M. Torres; co-supervisor: Natalia Martins. Defended and approved 12-Oct-2012 http://hdl.handle.net/10773/10467