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 present… (More)
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)
In this paper, we consider the third-order nonlinear neutral delay dynamic equations n B(t) ˆ A(t) ` y(t) + p(t)y(τ (t)) ´ ∆ ˜ ∆ o ∆ + Z b a F (t, ξ, y(g(t, ξ))) ∆ξ = 0, on an arbitrary time scale T which is unbounded above. We establish some sufficient conditions which ensure that every solution of the above equations oscillates or converges to zero. To… (More)
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.