Qualitative analysis of dynamic equations on time scales

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dc.contributor.authorAbbas, Syed
dc.date.accessioned2022-01-07T19:54:50Z
dc.date.available2022-01-07T19:54:50Z
dc.date.issued2018-02-20
dc.description.abstractIn 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.departmentMathematics
dc.formatText
dc.format.extent13 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationAbbas, S. (2018). Qualitative analysis of dynamic equations on time scales. <i>Electronic Journal of Differential Equations, 2018</i>(51), pp. 1-13.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/15107
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.holderThis work is licensed under a Creative Commons Attribution 4.0 International License.
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2018, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectDynamic equations
dc.subjectTime scale calculus
dc.subjectWeierstrass M-test
dc.subjectUniform convergence
dc.subjectPicard's iteration
dc.subjectEpsilon-approximate solution
dc.titleQualitative analysis of dynamic equations on time scales
dc.typeArticle

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