Basic Calculus on Time Scales and Some of Its Applications

Author

Martin Bohner, Missouri University of Science and TechnologyFollow
Ravi P. Agarwal

Abstract

The study of dynamic systems on time scales not only unifies continuous and discrete processes, but also helps in revealing diversities in the corresponding results. In this paper we shall develop basic tools of calculus on time scales such as versions of Taylor's formula, l'Hôspital's rule, and Kneser's theorem. Applications of these results in the study of asymptotic and oscillatory behavior of solutions of higher order equations on time scales are addressed. As a further application of Taylor's formula, Abel-Gontscharoff interpolating polynomial on time scales is constructed and best possible error bounds are offered. We have also included notes at the end of each section which indicate further scope of the calculus developed in this paper.

Recommended Citation

M. Bohner and R. P. Agarwal, "Basic Calculus on Time Scales and Some of Its Applications," Results in Mathematics, Springer Verlag, Jan 1999.

The definitive version is available at https://doi.org/10.1007/BF03322019

Department(s)

Mathematics and Statistics

Keywords and Phrases

time scales; Taylor's theorem; l'Hôspital's rule; kneeser's Theorem; Abel-Gontscharoff interpolation

International Standard Serial Number (ISSN)

1422-6383

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 1999 Springer Verlag, All rights reserved.

Publication Date

01 Jan 1999