Qualitative analysis of dynamic equations on time scales
Date
2018-02-20
Authors
Abbas, Syed
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, we establish the Picard-Lindelof theorem and approximating results for dynamic equations on time scale. We present a simple proof for the existence and uniqueness of the solution. The proof is produced by using convergence and Weierstrass M-test. Furthermore, we show that the Lispchitz condition is not necessary for uniqueness. The existence of epsilon-approximate solution is established under suitable assumptions. Moreover, we study the approximate solution of the dynamic equation with delay by studying the solution of the corresponding dynamic equation with piecewise constant argument. We show that the exponential stability is preserved in such approximations.
Description
Keywords
Dynamic equations, Time scale calculus, Weierstrass M-test, Uniform convergence, Picard's iteration, Epsilon-approximate solution
Citation
Abbas, S. (2018). Qualitative analysis of dynamic equations on time scales. <i>Electronic Journal of Differential Equations, 2018</i>(51), pp. 1-13.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.