Symmetric Quantum Calculus

Name: Symmetric Quantum Calculus
Creator: da Cruz, Artur M. C. Brito
Keywords: 34N05, 39A12, 39A13, 49K05, 49K15, Mathematics - Classical Analysis and ODEs, Optimization and Control (math.OC), Classical Analysis and ODEs (math.CA), FOS: Mathematics, 0101 mathematics, Mathematics - Optimization and Control, 01 natural sciences

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2013Embargo end date: 01 Jan 2013Publisher:arXivFunded by:FCT | CÁLCULO QUÂNTICO SIMÉTRIC...

Authors: da Cruz, Artur M. C. Brito;

doi: 10.48550/arxiv.1306.1327

arXiv: 1306.1327

Symmetric Quantum Calculus

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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 $��,��$-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-$��$ integral on time scales.

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

Keywords

34N05, 39A12, 39A13, 49K05, 49K15, Mathematics - Classical Analysis and ODEs, Optimization and Control (math.OC), Classical Analysis and ODEs (math.CA), FOS: Mathematics, Mathematics - Optimization and Control

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