* Correspondence: [email protected]; [email protected] Yangtze Center of Mathematics, Sichuan University, Chengdu 610064, P. R. China Full list of author information is available at the end of the article Abstract In this paper, we consider a class of impulsive difference equations with distributed delays. By establishing an impulsive delay difference inequality and using the propertie...

Based on Riccati transformation and the inequality technique, we establish some new sufficient conditions for oscillation of the second-order neutral delay dynamic equations on time scales. Our results not only extend and improve some known theorems, but also unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation ...

In this paper we shall discuss the exponential stability in mean square for a neutral stochastic diierential diierence equation of the form dx(t) ? G(x(t ?))] = f(t; x(t); x(t ?))dt + (t; x(t); x(t ?))dw(t). In the case when (t; x; y) 0 this neutral stochastic diierential diierence equations becomes a deterministic neutral diierential diierence equations d dt x(t)?G(x(t?))] = f(t; x(t); x(t?))....

On the one hand, periodic boundary value problems PBVPs for short for differential equations and difference equations have received much attention in the literature. See, for example, 1–17 and references therein. On the other hand, recently, the study of dynamic equations on time scales has became a new important branch see, e.g., 18–22 . Naturally, some authors have focused their attention on ...

We exhibit an alternative method for solving inhomogeneous second–order linear ordinary dynamic equations on time scales, based on reduction of order rather than variation of parameters. Our form extends recent (and long-standing) analysis on R to a new form for difference equations, quantum equations, and arbitrary dynamic equations on time scales.

We characterize the probability distributions of finite all order moments having generating functions for orthogonal polynomials of ultraspherical type. 1. Motivation: Meixner families There is a one to one correspondance between probability distributions on the real line and polynomials of a one variable satisfying a three-terms recurrence relation subject to some positive conditions ([9]). Th...

In a wide subclass of generalized order statistics, representations of marginal density and distribution functions are developed. The results are applied to obtain several relations, such as recurrence relations, and explicit expressions for the moments of generalized order statistics from Pareto, power function and Weibull distributions. Moreover, characterizations of exponential distributions...

Introducing shift operators on time scales we construct the integro-dynamic equation corresponding to the convolution type Volterra differential and difference equations in particular cases T = R and T = Z. Extending the scope of time scale variant of Gronwall’s inequality we determine function bounds for the solutions of the integro dynamic equation.

This note provides new quantitative bounds for the recursive equation yn+1 = A + yn yn−k , n = 0, 1, . . . , where y−k , y−k+1, . . . , y−1, y0, A ∈ (0,∞) and k ∈ {2, 3, 4, . . .}. Issues regarding exponential convergence of solutions are also considered. In particular, it is shown that exponential convergence holds for all (A, k) for which global asymptotic stability was proven in [R.M. Abu-Sa...

A nonlinear integro-differential equation of convolution type with order of nonlinearity more than one and a stable trivial solution is considered. The integral in this equation has an exponential kernel and polynomial integrand. The difference analogue of the equation considered is constructed in the form of a difference equation with continuous time and it is shown that this difference analog...