This book provides a comprehensive and systematic approach to the study of the qualitative
theory of boundedness, periodicity, and stability of Volterra difference equations. The book …

We address the study of well posedness on Lebesgue spaces of sequences for the following
fractional semidiscrete model with finite delay (0.1) Δ α u (n)= T u (n)+ β u (n− τ)+ f (n), n∈ N …

Let T be an arbitrary time scale that is unbounded above. By means of a variation of
Lyapunov's method and contraction mapping principle this paper handles asymptotic …

In this paper, we use what we call the shift operator so that general delay dynamic equations
of the form\[x^{\Delta}(t)= a (t) x (t)+ b (t) x (\delta_ {-}(h, t))\delta_ {-}^{\Delta}%(h …

The book provides an integrated approach to the study of the qualitative theory of dynamical
systems on time scales. It is aimed at postgraduate students and researchers with basic …

We propose a new area of mathematics, namely stochastic dynamic equations, which
unifies and extends the theories of stochastic differential equations and stochastic difference …

General nonlinear difference equations with time‐varying delays are considered. Explicit
criteria for contraction of such equations are presented. Then some simple sufficient …

1 Introduction Page 1 Electronic Journal of Qualitative Theory of Differential Equations 2009,
No. 8, 1-7; http://www.math.u-szeged.hu/ejqtde/ Stability in discrete equations with variable …

In this article, the contraction mapping principle and Liapunov's method are used to study
qualitative properties of nonlinear Volterra equations of the form x (t)= a (t)−∫ t 0 C (t, s) g (s …

We use the modification of Krasnoselskii's fixed point theorem due to TA Burton ([1] Theorem
3) to show that the totally nonlinear difference equation with functional delay Δx (t)=-a (t) x< …