Dynamic equations on time scales: a survey
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In this article, the authors give an introduction to the time scales calculus, and present various properties of the exponential function on an arbitrary time scale, and use it to solve linear dynamic equations of first order.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2002-04-01 and is currently open access. It has received 575 citations till now. The article focuses on the topics: Time-scale calculus & Independent equation.read more
Citations
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Dynamic Equations on Time Scales: An Introduction with Applications
Martin Bohner,Allan Peterson +1 more
TL;DR: The Time Scales Calculus as discussed by the authors is a generalization of the time-scales calculus with linear systems and higher-order linear equations, and it can be expressed in terms of linear Symplectic Dynamic Systems.
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Inequalities on Time Scales: A Survey
TL;DR: In this article, the authors present time scales versions of the inequalities: Holder, Cauchy-Schwarz, Minkowski, Jensen, Gronwall, Bernoulli, Bihari, Opial, Wirtinger, and Lyapunov.
Book
Nonoscillation and Oscillation Theory for Functional Differential Equations
TL;DR: In this paper, the qualitative theory of differential equations with or without delays is summarized, collecting recent oscillation studies important to applications and further developments in mathematics, physics, engineering, and biology.
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Stability for time varying linear dynamic systems on time scales
TL;DR: In this article, conditions under which the solutions of a time varying linear dynamic system of the form xΔ(t)=A(t)x (t) are stable on certain time scales were studied.
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Oscillation of Second Order Nonlinear Dynamic Equations on Time Scales
Samir H. Saker,Martin Bohner +1 more
TL;DR: By means of Riccati transformation techniques, the authors established some oscillation criteria for a second order nonlinear dynamic equation on time scales in terms of the coefficients, and gave examples of dynamic equations to which previously known oscillation rules are not applicable.
References
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Book
Dynamic Equations on Time Scales: An Introduction with Applications
Martin Bohner,Allan Peterson +1 more
TL;DR: The Time Scales Calculus as discussed by the authors is a generalization of the time-scales calculus with linear systems and higher-order linear equations, and it can be expressed in terms of linear Symplectic Dynamic Systems.
Book
An introduction to difference equations
TL;DR: In this article, the authors combine both analytic and geometric (topological) approaches to studying difference equations and integrate both classical and modern treatments of the subject, offering material stability, z-transform, discrete control theory and symptotic theory.