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arXiv · 1306.1327

Symmetric Quantum Calculus

Artur M. C. Brito da Cruz
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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 $\alpha,\beta$-symmetric, the $q$-symmetric, and the Hahn symmetric quantum calculus. We introduce the symmetric quantum variational calculus and an Euler-Lagrange type equation for the $q$-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-$\alpha$ integral on time scales.

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Artur M. C. Brito da Cruz. 2013-06-06. Symmetric Quantum Calculus. https://arxiv.org/abs/1306.1327

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