Dynamic systems in many branches of science and industry are often perturbed by various types of environmental noise. Analysis of this class of models are very popular among researchers. In this paper, we present a method for approximating solution of fractional-order stochastic delay differential equations driven by Brownian motion. The fractional derivatives are considered in the Caputo sense...

We investigate how the behaviour, especially at 1; of continuous real solutions f (t) to the equation f (t) = a 1 f (t + h 1) + a 2 f (t ? h 2); where a 1 ; a 2 ; h 1 ; h 2 are positive real constants, depends on the values of these parameters. Deenitive answers are given, except in certain cases when h 1 =h 2 is rational..

A novel and eective method based on Haar wavelets and Block Pulse Functions(BPFs) is proposed to solve nonlinear Fredholm integro-dierential equations of fractional order.The operational matrix of Haar wavelets via BPFs is derived and together with Haar waveletoperational matrix of fractional integration are used to transform the mentioned equation to asystem of algebraic equations. Our new met...

Abstract: A new method to solve a Lyapunov equation for a discrete delay system is proposed. Using this method, a Lyapunov equation can be solved from a simple linear equation and N -th power of a constant matrix, where N is the state delay. Combining a Lyapunov equation and frequency domain stability, a new stability condition is proposed for a discrete state delay system whose state delay is ...

The delay Lyapunov equation is an important matrix boundary-value problem which arises as an analogue of the Lyapunov equation in the study of time-delay systems ẋ(t) = A0x(t) +A1x(t− τ) +B0u(t). We propose a new algorithm for the solution of the delay Lyapunov equation. Our method is based on the fact that the delay Lyapunov equation can be expressed as a linear system of equations, whose unkn...

This paper studies the existence of periodic solutions to the delay differential equation ẋ(t) = f(x(t− μτ(t)), ) . The analysis is based on a perturbation method previously used for retarded differential equations with constant delay. By transforming the studied equation into a perturbed non-autonomous ordinary equation and using a bifurcation result and the Poincaré procedure for this last eq...

Abstract: The report evolves a method, which uses the formalization and results of positional antagonistic dierential games theory, developed by N. N. Krasovskii and his scienti c school, for constructing solutions of a class of non-antagonistic dierential games. The method transforms non-antagonistic game into so-called non-standard optimal control problem. Numerical solutions for Stackelberg ...