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 solvedelay differential equations and time-delay system. the method is based upon ex...

Introduction: The theory and application of linear and nonlinear delay differential equations is an important subject within physics and applied mathematics. There are several numerical approaches for solving linear and nonlinear delay differential equations. Aim: In this paper, differential transform method ( DTM ) is applied to numerical solution of linear and nonlinear delay differential equ...

Uncertain delay differential equation is a type of differential equations driven by a canonical Liu process. This paper mainly focuses on the stability of uncertain delay differential equations. At first, the concept of stability in measure, stability in mean and stability in moment for uncertain delay differential equations will be presented. In addition, the sufficient condition for uncertain...

The second-order delay differential equations often appear in the dynamical system, celestial mechanics, kinematics, and so forth. Some numerical methods for solving secondorder delay differential equations have been discussed, which include θ-method [1], trapezoidal method [2], and RungeKutta-Nyströmmethod [3].The variational iteration method (VIM) was first proposed by He [4, 5] and has been ...

This paper summarizes recent research on an approach for the analytical solution to systems of delay differential equations developed using the Lambert W function [26, 29], and its applications [25, 28]. Also, several outstanding research problems associated with the solution of systems of delay differential equations using the matrix Lambert W function are highlighted. The solution has the for...

semilinear stochastic evolution equations with multiplicative l'evy noise are considered‎. ‎the drift term is assumed to be monotone nonlinear and with linear growth‎. ‎unlike other similar works‎, ‎we do not impose coercivity conditions on coefficients‎. ‎we establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. ‎as corollarie...

The current final project belongs to a subject in the master’s degree in Advanced Mathematics at the University of Barcelona. It deals with time delays which usually are arisen in differential equations. Firstly, the project develops the main important known results of Delay Differential Equations, which are a specific case of Functional Differential Equations. In particular, we shall also focu...

where W is a Wiener process, Z is a Hölder continuous process with Hölder exponent greater than 1/2, the coefficients a, b, c depend on the past of the process X . The integral with respect to W is understood in the usual Itô sense, while the one with respect to Z is understood in the pathwise sense. (A precise definition of all objects is given in Section 2.) We will call this equation a mixed...