Qualitative analysis of dynamic equations on time scales
dc.contributor.author | Abbas, Syed | |
dc.date.accessioned | 2022-01-07T19:54:50Z | |
dc.date.available | 2022-01-07T19:54:50Z | |
dc.date.issued | 2018-02-20 | |
dc.description.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. | |
dc.description.department | Mathematics | |
dc.format | Text | |
dc.format.extent | 13 pages | |
dc.format.medium | 1 file (.pdf) | |
dc.identifier.citation | Abbas, S. (2018). Qualitative analysis of dynamic equations on time scales. Electronic Journal of Differential Equations, 2018(51), pp. 1-13. | |
dc.identifier.issn | 1072-6691 | |
dc.identifier.uri | https://hdl.handle.net/10877/15107 | |
dc.language.iso | en | |
dc.publisher | Texas State University, Department of Mathematics | |
dc.rights | Attribution 4.0 International | |
dc.rights.holder | This work is licensed under a Creative Commons Attribution 4.0 International License. | |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
dc.source | Electronic Journal of Differential Equations, 2018, San Marcos, Texas: Texas State University and University of North Texas. | |
dc.subject | Dynamic equations | |
dc.subject | Time scale calculus | |
dc.subject | Weierstrass M-test | |
dc.subject | Uniform convergence | |
dc.subject | Picard's iteration | |
dc.subject | Epsilon-approximate solution | |
dc.title | Qualitative analysis of dynamic equations on time scales | |
dc.type | Article |