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Abstract. The study of dynamic equations on time scales, which goes back to its founder Stefan Hilger (1988), is an area of mathematics which is currently receiving considerable attention. Although the basic aim of this is to unify the study of differential and difference equations, it also extends these classical cases to “in between”. In this paper we… (More)

- MARTIN BOHNER, OLEXANDR M. STANZHYTSKYI, ANASTASIIA O. BRATOCHKINA, Stefan Hilger, Suman Sanyal
- 2013

In this article, we construct stochastic integral and stochastic differential equations on general time scales. We call these equations stochastic dynamic equations. We provide the existence and uniqueness theorem for solutions of stochastic dynamic equations. The crucial tool of our construction is a result about a connection between the time scales… (More)

- DA-XUE CHEN, JIE-CHUN LIU, Stefan Hilger

In this paper, we consider the third-order nonlinear neutral delay dynamic equations

- Lynn Erbe, Taher S. Hassan, Allan Peterson, Samir H. Saker, S. Saker, Stefan Hilger
- 2009

This paper is concerned with oscillation of the second-order half-linear delay dynamic equation (r(t)(x)) + p(t)x(τ(t)) = 0, on a time scale T where 0 < γ ≤ 1 is the quotient of odd positive integers, p : T → [0,∞), and τ : T → T are positive rd-continuous functions, r(t) is a positive and (delta) differentiable function, τ(t) ≤ t, and lim t→∞ τ(t) = ∞. We… (More)

- Georg Heike, Reinhold Greisbach, Stefan Hilger, Bernd J. Kröger
- EUROSPEECH
- 1989

- Stefan Hilger
- 1988

- Stefan Hilger, Galina Filipuk, +5 authors R. A. Kycia
- 2014

In this paper we shall study the problem of the (q, h)-discretization (generalization) of ladder operators. We shall present a few illustrative and important examples including the Weber, Bessel and Laguerre ladders and their (q, h)-analogues. AMS Subject Classifications: 39A10, 81S05.

- S. Hilger, P. E. Kloeden
- 1993

Variability in the underlying time structure of dynamical systems and its consequences are encountered in a variety of mathematical contexts, though are not always recognized as such. An obvious example is the numerical time-discretization of ordinary differential equations, where the relationship between the behaviour of an approximate discrete-time… (More)

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