School of Basic Sciences
Indian Institute of Technology Mandi
Kamand (H.P.) - 175 005, India
email: abbas@iitmandi.ac.in
Syed Abbas
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.
Submitted August 8, 2017. Published February 20, 2018.
Math Subject Classifications: 34N05, 26E70, 34A12.
Key Words: Dynamic equations; time scale calculus; Weierstrass M-test;
uniform convergence; Picard's iteration; epsilon-approximate solution.
Show me the PDF file (234 KB), TEX file for this article.
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Syed Abbas School of Basic Sciences Indian Institute of Technology Mandi Kamand (H.P.) - 175 005, India email: abbas@iitmandi.ac.in |
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