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Nabla dynamic equations on time scales

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Bibliographic Details
Title: Nabla dynamic equations on time scales
Authors: Anderson, Douglas, Bullock, John, Erbe, Lynn, Peterson, Allan, Tran, Hoainam
Publisher Information: International Publications, Toledo, OH
Subject Terms: Nabla derivative, Time-scale analysis and singular perturbations in control/observation systems, measure chain, time scale, Nabla exponential functions, hyperbolic and trigonometric functions, linear dynamic equations, Discrete version of topics in analysis, Hermitian systems, Exponential and trigonometric functions
Description: The authors translate some well known features from the calculus on time scales to the backward time case. They consider properties of the so called Nabla derivative, \(\nu\) regressivity, certain corresponding algebraic structures, Nabla exponential functions, hyperbolic and trigonometric functions. Also some results on positivity and sign changes of the Nabla exponential function are derived, the exponential function is computed for some special examples of time scales. In the last two chapters the linear theory for Nabla dynamic equations (scalar and matrix case) is presented.
Document Type: Article
File Description: application/xml
Access URL: https://zbmath.org/1902544
Accession Number: edsair.c2b0b933574d..34e560501692e3875139860881331e3c
Database: OpenAIRE
Description
Abstract:The authors translate some well known features from the calculus on time scales to the backward time case. They consider properties of the so called Nabla derivative, \(\nu\) regressivity, certain corresponding algebraic structures, Nabla exponential functions, hyperbolic and trigonometric functions. Also some results on positivity and sign changes of the Nabla exponential function are derived, the exponential function is computed for some special examples of time scales. In the last two chapters the linear theory for Nabla dynamic equations (scalar and matrix case) is presented.