This paper proposes a new computational scheme for approximating variable-order fractional integral operators by means of finite element scheme. This strategy is extended to approximate the solution of a class of variable-order fractional nonlinear systems with time-delay. Numerical simulations are analyzed in the perspective of the mean absolute error and experimental convergence order. To ill...

A PID-deadtime controller is realized by inserting a time delay into the integral feedback circuit. Such a controller possesses a transfer function similar to a Smith predictor or an internal-model controller. Effective tuning of PID deadtime controllers remains unsolved even though they give better regulatory performance than a conventional PID control algorithm for processes with a long pure ...

Abstract: In this paper, some new delay integral inequalities with two independent variables on time scales are established, which can be used as a hand tool in the investigation of qualitative properties of solutions of delay dynamic equations on time scales. Some applications for the established inequalities are also presented, and new explicit bounds on unknown functions of delay dynamic equ...

In this paper, we investigate some nonlinear delay integral inequalities and their analogues which provide explicit bounds on unknown functions. The inequalities given here can be used as tools in the qualitative theory of certain delay differential equations, delay integral equations and delay difference equations.

in this article differential transformation method (dtms) has been used to solve neutral functional-differential equations with proportional delays. the method can simply be applied to many linear and nonlinear problems and is capable of reducing the size of computational work while still providing the series solution with fast convergence rate. exact solutions can also be obtained from the kno...

We are concerned with the exponential mean-square stability of two-step Maruyama methods for stochastic differential equations with time delay. We propose a family of schemes and prove that it can maintain the exponential mean-square stability of the linear stochastic delay differential equation for every step size of integral fraction of the delay in the equation. Numerical results for linear ...

In this paper we are going to study the Hyers{Ulam{Rassias typesof stability for nonlinear, nonhomogeneous Volterra integral equations with delayon nite intervals.