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.
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| Syed Abbas |
School of Basic Sciences
Indian Institute of Technology Mandi
Kamand (H.P.) - 175 005, India
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