So far there are not many results on the stability for stochastic functional differential equations with infinite delay. Themain aim of this paper is to establish some new criteria on the stability with general decay rate for stochastic functional differential equations with infinite delay. To illustrate the applications of our theories clearly, this paper also examines a scalar infinite delay ...

Stochastic delay differential equations allow the stochastic differential equations to incorporate past data segments. They are widely used to solve systems having delay feedbacks. In the linear Gaussian case, the differential equations can be solved by computing the covariance functions through the double Laplace transform. It turns out that the solution can be decomposed into the sum of indep...

This paper is concerned with a class of linear impulsive delay differential equations. Asymptotic stability of analytic solutions of this kind of equations is studied by the property of delay differential equations without impulsive perturbations. New numerical methods for this kind of equations are constructed. The convergence and asymptotic stability of the methods for this kind of equations ...

This paper studies the oscillation properties of higher order impulsive delay differential equations, and some sufficient conditions for all bounded solutions of this kind of higher order impulsive delay differential equations to be nonoscillatory are obtained by using a comparison theorem with corresponding nonimpulsive differential equations. AMS subject classification: 34C10, 34C15.

In this paper, we introduce hybrid of block-pulse functions and Bernstein polynomials and derive operational matrices of integration, dual, differentiation, product and delay of these hybrid functions by a general procedure that can be used for other polynomials or orthogonal functions. Then, we utilize them to solve delay differential equations and time-delay system. The method is based upon e...

‎This article develops a direct method for solving numerically‎ ‎multi delay-fractional differential and integro-differential equations‎. ‎A Galerkin method based on Legendre polynomials is implemented for solving‎ ‎linear and nonlinear of equations‎. ‎The main characteristic behind this approach is that it reduces such problems to those of‎ ‎solving a system of algebraic equations‎. ‎A conver...

In this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in F(t,x(t))dt +G(t,x(t))dW_t$ in which the multifunction $F$ is semimonotone and hemicontinuous and the operator-valued multifunction $G$ satisfies a Lipschitz condition. We define the It^{o} stochastic integral of operator set-valued stochastic pr...